Interdependent Self-Organizing - IA de Investigación especializada en el MIT

Interdependent Self-Organizing
Mechanisms for Cooperative
Survival

Abstract Cooperative survival “games” are situations in which,
during a sequence of catastrophic events, no one survives unless
everyone survives. Such situations can be further exacerbated by
uncertainty over the timing and scale of the recurring catastrophes,
while the resource management required for survival may depend
on several interdependent subgames of resource extraction,
distribución, and investment with conﬂicting priorities and
preferences between survivors. In social systems, self-organization
has been a critical feature of sustainability and survival; por lo tanto,
in this article we use the lens of artiﬁcial societies to investigate
the effectiveness of socially constructed self-organization for
cooperative survival games. We imagine a cooperative survival
scenario with four parameters: escala, eso es, n in an n-player game;
incertidumbre, with regard to the occurrence and magnitude of each
catastrophe; complejidad, concerning the number of subgames to be
simultaneously “solved”; and opportunity, with respect to the
number of self-organizing mechanisms available to the players. Nosotros
design and implement a multiagent system for a situation composed
of three entangled subgames—a stag hunt game, a common-pool
resource management problem, and a collective risk dilemma—and
specify algorithms for three self-organizing mechanisms for
governance, trading, and forecasting. A series of experiments shows,
as perhaps expected, a threshold for a critical mass of survivors and
also that increasing dimensions of uncertainty and complexity
require increasing opportunity for self-organization. Perhaps less
expected are the ways in which self-organizing mechanisms may
interact in pernicious but also self-reinforcing ways, highlighting the
need for some reﬂection as a process in collective self-governance for
cooperative survival.

Matthew Scott*
Imperial College London
Department of Electrical and

Electronic Engineering

matthew.scott18@imperial.ac.uk

Jeremy Pitt
Imperial College London
Department of Electrical and
Electronic Engineering

Palabras clave
Artiﬁcial societies, multiagent systems,
self-organization, cooperative survival
juegos

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1 Introducción

Cooperative survival “games” are situations in which, following a catastrophic event, no one
survives unless everyone survives. Elements of such situations feature prominently in computer
games and board games but have been more seriously and extensively studied in sociology and an-
thropology, especially with regard to societies surviving in difﬁcult or hostile environments (p.ej.,
Briggs, 1970; Norberg-Hodge, 1991). Similar features appear in embedded cyberphysical systems,

* Autor correspondiente.

METRO. Scott and J. Pitt

Mechanisms for Cooperative Survival

such as ad hoc networks and sensor networks (Durmus et al., 2011); evolutionary systems needing
to reconﬁgure themselves after a dramatic change in their operating environments (Pitt & Hart,
2017); and sociotechnical systems, such as community energy systems, relying on renewable energy,
where attention and collective action may be required to prevent a generation shortfall leading to a
brownout or blackout (Bourazeri & Pitt, 2018).

These situations can be further exacerbated by uncertainty over the timing and scale of the catas-
trophe (Domingos et al., 2020) and the overall game itself being composed of multiple subgames of
resource extraction, resource distribution, and resource investment, each with conﬂicting priorities
and preferences (Bekius et al., 2022). Por ejemplo, in a situation prone to ﬂooding, investing too
many resources into ﬂood defenses wastes utility, but investing too few can be fatal or cost more
in the long term. When there are multiple codependent communities, there may be multiple inter-
acting common-pool resource (CPR) management problems operating on different timescales. Para
ejemplo, an irrigation system serving multiple communities may have both an appropriation prob-
lem and a maintenance problem: If one community appropriates excessively, then the others may
not contribute to maintenance, to the detriment of all (Ostrom, 1990). Similar timing and structural
problems have been observed in other agricultural settings (Lansing & Kremer, 1993).

In this article, we specify a scenario based on an archipelago of islands, each of which needs
the others to survive recurring disasters. We deﬁne an iterated cooperative survival game composed
of three interdependent subgames: a stag hunt game, a CPR management problem, and a collec-
tive risk dilemma (CRD). The stag hunt subgame (Carlsson & van Damme, 1993) is an n-player
cooperative resource extraction game with limitations: Por ejemplo, it is possible to exhaust the
resource by overhunting. This subgame precedes a resource distribution subgame that is an n-player
CPR management problem (Ostrom, 1990) in which the players have to decide, individually and
collectively, how much of these hunted resources should be provisioned to, and appropriated from,
a common pool. This problem in turn precedes a resource investment subgame that is an n-player
CRD (Domingos et al., 2020) in which the players have to decide how much of their appropri-
ated resources are used to mitigate the next catastrophic event. Failure to do so determines their
ability to participate effectively in the subsequent iteration. Underpinning these subgames are the
goals of the cooperative survival game, a saber, not just for all to survive but also to ﬁnd a mu-
tually acceptable balance between individual and collective goals, Por ejemplo, between individual
cognitive effort and quality of the overall outcome in information processing (Nowak et al., 2020)
or between engagement in personally valued pursuits and participation in socially productive duties
for self-governance (Ober, 2017).

To address this cooperative survival scenario and its component subgames, we use the lens of
artiﬁcial societies (Powers, 2018) to design three interdependent, socially constructed self-organizing
mechanisms, one each for governance, trading, and forecasting. This is based on the observation
eso, in previous work, each mechanism has been targeted at one game, with forecasting derisking
the CRD (Domingos et al., 2020), governance informing the CPR management (Ostrom, 1990), y
gifting for redistributing inequalities and creating a form of social capital (Malinowski, 1920). Por
socially constructed, we mean that these mechanisms are intrasubjective agreements based on net-
worked interaction and communication (Berger & Luckmann, 1966), producing conceptual re-
sources, such as trust, institutions, and reciprocity, that have been shown to enhance opportunities
for successful collective action (Ostrom & Ahn, 2003; Petruzzi et al., 2017).

Como consecuencia, the challenge becomes as follows: Rather than one mechanism solving each subgame
separately, what combination of which form of these self-organizing mechanisms “optimally solves” the cooperative
survival game under different dimensions of scale, incertidumbre, and constraints?

Respectivamente, this article is structured as follows. Sección 2 describes the nature of both the co-
operative survival games and the means of self-organization. We approach the former from the
perspective of utility calculations and the dilemma faced when attempting to tackle these problems.
Following this, we describe the system that we propose in section 3 as a means of investigating the
problem of cooperative survival as construed here, as well as the codiﬁcation of the various system
elements in section 4.

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Mechanisms for Cooperative Survival

Sección 5 presents a series of experiments of increasing uncertainty over the dimensions of the
catastrophe, scale of the system, and constraints on the availability of the different self-organizing
mechanisms. The results of these experiments show that this problem is solvable, as long as there is a
sufﬁcient number of players and the availability of self-organizing mechanisms is judiciously selected
due to the possibility of both mutually reinforcing and pernicious interactions. Además, con
increasing levels of uncertainty in the system, increasing opportunities for such self-organizations
son requeridos. After a consideration of related and further work in section 6, we conclude in section 7
by arguing that the dependencies between subgames and self-organizing mechanisms exist not only
between each other but among themselves as well, in complex ways, highlighting the need for
reﬂection as an essential process in collective self-governance for cooperative survival.

2 Cooperative Survival Games and Self-Organization

This section presents the conceptual background to this work, covering cooperative survival
games and the parameters of scale, incertidumbre, complejidad, and opportunity (mechanisms for self-
organización). It starts in section 2.1 with an informal description of cooperative survival games from
different viewpoints. Sobre esta base, sección 2.2 introduces the speciﬁc scenario used in this work
and establishes the parameters of scale and uncertainty, while section 2.3 establishes the dimen-
sion of complexity with a review of three interdependent games: a stag hunt game, a public goods
juego, and a CRD. Finalmente, sección 2.4 presents the opportunities available to the agents—three
self-organizing mechanisms of trading, pronóstico, and governance—which essentially create meta-
level political games that may defuse an “inevitable tragedy” or change the constraints inherent
in an object-level resource competition game (Ostrom, 1990).

2.1 Cooperative Survival Games
An instance of cooperative survival can be found in the genre of computer games in which players
must work together to survive in an open, hostile environment. It is also the basic premise of
round-based board games like Escape the Dark Castle and Ravine, where a crucial feature of game
play is the need to keep enough players alive in any one round to gather sufﬁcient resources to ensure
that even the weakest players survive and can participate in resource gathering in the subsequent
round.

Además, cooperative survival is a phenomenon witnessed in many aspects of “real life.” Human
beings are a social (y, en efecto, cooperative) species that relies on cooperation to survive and thrive
(Bowles & Gintis, 2011), and in anthropology, there are many examples of survival even in extremely
hostile environments (p.ej., Briggs, 1970; Norberg-Hodge, 1991).

Sin embargo, the capability to overcome CRDs is demonstrated from a young age, where children
as young as six years old can spontaneously ﬁnd ways to collaborate to maintain a shared, lim-
ited resource. This was shown in the context of a common pool of resources paradigm involving
a shared water source in which children were capable of collectively preventing resource collapse
by creating inclusive rules, equally distributing the rewards and distracting one another from the
delay-of-gratiﬁcation task (Koomen & Herrmann, 2018). Además, children can be seen to dis-
play notions of fairness from a young age as well, making sacriﬁces for fairness when they have less
than others, when others have been unfair, and when they have more than others. This goes against
rational self-interest for the good of cooperation (McAuliffe et al., 2017).

Similar features of cooperative behavior for individual or collective survival can be observed
in cyberphysical and sociotechnical systems. In cyberphysical systems, Por ejemplo, there can be a
trade-off between accuracy and longevity in a sensor network (Nikoloska & Simeone, 2021) y
between quality of service (QoS) and end-to-end connectivity in an ad hoc network. In a sensor
network, to maximize the objective of accuracy, all sensors should be transmitting all the time,
but to maximize the objective of longevity, only enough sensors needed for acceptable accuracy
should be taking measurements and transmitting signals; ideally, only those sensors with the most
resources would measure and transmit, to avoid “exhausting” nodes with fewer resources, cual

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METRO. Scott and J. Pitt

Mechanisms for Cooperative Survival

would thereby threaten the network as a whole. Similarmente, in an ad hoc network, to maximize through
put, as many nodes as possible should be operative, but to ensure the objective of end-to-end
conectividad, only enough nodes needed for acceptable QoS should be forwarding packets. There is
considerable interest in the notion of resilience in such systems, particularly with regard to disaster
respuesta (Ti et al., 2022).

Elements of cooperative survival can also be seen in some sociotechnical systems, Por ejemplo,
a community energy system (Pitt et al., 2014). Energy self-sufﬁciency in a community energy system
redirects the onus of resource management from the demand side (global generators must match the
request made by all consumers) to the supply side (local consumers distribute the available energy
generated from their own sources). This converts the problem to sustainable management of a CPR
(es decir., a public good) that is both ﬁnite and might be insufﬁcient to meet demand, otherwise there will
be a brownout or, worse, a blackout. Este, entonces, would seem to create the conditions for a tragedy
of the commons: One person alone has no incentive to voluntarily reduce their demand to avoid
the outage, because unless everyone else also reduces their demand, the sole volunteer loses utility
in the short term and still suffers the same tragedy as everyone else. Therefore there needs to be
some intervention, such as self-governing institutions (Ostrom, 1990), which have been shown to
enable (humano) participants to avoid the supposedly inevitable tragedy of the commons.

It is worth noting that the cooperative survival game Minecraft allows the speciﬁcation of various
mods and plug-ins: It has been observed that sustainable Minecraft hosts have implemented mods
and plug-ins that reproduce the features of Ostrom’s self-governing institutions (Frey & Sumner,
2018). En otras palabras, cooperative survival can be negotiated even by (anecdotally) most antisocial
groups given sufﬁcient incentive and adequate opportunity for social construction of a solution.

2.2 Scenario Speciﬁcation
On the basis of this general discussion of cooperative survival games, the cooperative survival sce-
nario proposed for this article is illustrated in Figure 1. We imagine an archipelago of islands that
regularly have to cooperate to mitigate disaster in the form of a randomly located earthquake with
an epicenter limited to the bounds of the archipelago. The location, magnitude, and timing of the
earthquake are unknown; therefore how badly a disaster affects each island depends on its distance
from the epicenter and on the magnitude and timing. To mitigate the disaster, the islands have
to contribute their personal resources to a common pool, cual, inconveniently, has the dual role

Cifra 1. Visualization of collective risk dilemma and archipelago.

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METRO. Scott and J. Pitt

Mechanisms for Cooperative Survival

of also serving as the communal fund, as islands may withdraw resources from it at will. Más-
más, to provision resources to the CPR, they have to participate in a resource extraction activity,
possibly in cooperation with other islands, to forage for either ﬁsh, yielding few resources at a low
riesgo, or deer, yielding more resources at a higher risk but requiring coordination between islands.
Islands must then decide how much to keep for themselves and how much to provision. If an is-
land’s personal resources fall below a critical level for a certain length of time, it will cease to exist
(the inhabitants will “die”).

The overall scenario can then be decomposed into several subgames: a resource gathering game
(es decir., a stag hunt game), a resource distribution game (es decir., a CPR management problem or linear
public goods game), and a resource contribution game (es decir., a disaster mitigation game or CRD).
Note that the interdependent subgames are designed to create a vicious circle or a virtuous spiral:
An inefﬁcient stag hunt yields fewer resources to distribute from the common pool, which provides
fewer resources for disaster mitigation and recovery, which can lead to an even more inefﬁcient stag
hunt (especially if islands “die”). En cambio, a more efﬁcient stag hunt provides more resources
for the common pool, providing more opportunity for disaster mitigation, maintaining critical mass
and creating social capital, which leads to a more efﬁcient stag hunt, etcétera. A less badly affected
island may help out one that is affected worse, helping to ensure its survival in the short term and
creating social capital for reciprocal behavior in the longer term.

Próximo, we brieﬂy review each type of game. Note that in the following discussion, an island in
the scenario is synonymous with a player in a subgame and is also synonymous with an agent in the
multiagent system to be developed in section 3.

2.3 Interdependent Games

2.3.1 Stag Hunt Game
A stag hunt game is an example of a two-player collective choice game that illustrates a conﬂict
between collectivity and individuality. In this game, two players are confronted with two forag-
ing options, for either a stag or a hare (although for contextual reasons, we use deer and ﬁsh,
respectivamente, in this article), and must choose which species to forage, both separately and with-
out the other’s knowledge. Choosing to forage for a stag will provide maximal rewards for both
parties, but only if the other player makes the same decision, else they will get nothing. Alterna-
activamente, choosing to forage for a hare will result in lesser returns but the guarantee to receive this
amount, as hares can be foraged individually. This article elects the payoff matrix for this game as
como se muestra en la figura 2. This formulation preserves the ordinality of the conventional stag hunt game
(es decir., (S, S) > (h, S) >= (h, h) > (S, h), for the row player); sin embargo, the numerical payoffs re-
sult from a combination of the utility functions detailed in section 4.5 and the scaling deﬁned in
sección 4.6.

For this article, we make several adjustments to the conventional stag hunt dilemma. To begin
con, we allow for all N players to play this game with a ﬁxed probability of catching a deer, resulting
in N/2 stag hunt games being played simultaneously.

Cifra 2. Payoff matrix for resource generation.

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METRO. Scott and J. Pitt

Mechanisms for Cooperative Survival

Además, we allow for repeated foraging of either ﬁsh or deer by introducing the concept of a
utility tier, akin to a step function, where more resources can be invested for a stochastic chance of
a higher yield, effectively multiplying payoffs (sección 4.5.3). De nuevo, this augments the conventional
utility calculation to incorporate the input resources.

Population dynamics also impact the ability to catch each animal. Despite the present-day issues
with ﬁsh sustainability, we assume that ﬁsh can multiply suitably fast to facilitate inﬁnite foraging.
This is designed to avoid the issue of permanent resource depletion, which would otherwise cause
the system to collapse trivially (es decir., we are concerned with contingently existential threats that are
avoidable by voluntary social construction, rather then necessarily existential threats that might re-
quire more draconian methods). En cambio, we both limit and impose a rate of reproduction on
the deer population. This has two effects: primero, it does allow the deer to be hunted into extinction,
dissuading continual foraging as a possible strategy, y segundo, it gives salience and comparison
to forecasting, where signaling must be used to communicate to other players that the resource is
nearing depletion and beneﬁt accrues to those players whose forecasts are most accurate.

After the set of games is complete, the total utility gained from all games (Ecuaciones 1 y 2) es

summed and redistributed proportionally to the total resources invested in the hunt (Ecuación 3).

The dilemma in this case is a matter of risk. Foraging ﬁsh allows for a guaranteed low return of
resources, whereas foraging for deer gives a lower chance at a higher payoff. Por esta razón, el
strategy for foraging ﬁsh is risk dominant, whereas the strategy for foraging deer is payoff dominant.
In a scenario where the survivability of the collective is paramount, the stag hunt game becomes
a problem of “risky coordination.” With few players coordinating for a high return, due to either
a small number of players or many players acting selﬁshly, survivability is hindered, as the weaker
players will be eliminated.

This leads to player utility being a function of foraging choice ci ∈ {d, F }, numerical payoff
Hc1,c2, the probability of a successful hunt p(ci), the number of participants N, the resources con-
tributed by each player to the forage ri, and the utility tier of the ﬁshing expedition UT(ri).

Por esta razón, we deﬁne the players’ utility function as follows. For N players i ∈ {1, . . . , norte}
forming N/2 iterated stag hunt games G ∈ {1, . . . , N/2} on each iterated round t ∈ {1, . . . , ∞}, nosotros
deﬁne the payoff (GRAMO(cid:4)

) of game G played by player i as

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GRAMO

(cid:4)
i

= Hci,cj

∗ p(ci) ∗ n(ci, ri)

norte(ci, ri) =

(cid:2)

UT(ri)

if ci = f
if ci = d

(1)

(2)

where n(ci, ri) represents the “number” of animals foraged, showing that only one deer may be
foraged per game, sin embargo, multiple ﬁsh can be foraged, depending on the utility tier (UT) discussed
in section 4.5.3. Además, cj represents the foraging choice for the second player playing the
stag hunt game. This provides the utility for each player as

ush
i

ri(cid:3)

norte
j=1 rj

norte(cid:4)

∗

j=1

GRAMO

(cid:4)
j

(3)

illustrating that the total utility a player receives from a foraging session is proportional to the
resources that they input. This results in two “temporary pools” being formed, one each for the stag
hunters and ﬁshermen, which are used to distribute resources according to Equation 3. This is not
to be confused with the common pool, which is permanently present for all players and is designed
as a reservoir for surplus resources.

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Mechanisms for Cooperative Survival

2.3.2 Common-Pool Resource Management
A CPR management problem is a type of iterated collective action situation that investigates the
issues concerning provision to and appropriation from a shared resource (Ostrom, 1990).

Regarding access, we consider two classiﬁcations: exclusivity, which concerns the ability to ex-
clude individuals from the beneﬁts of the resource, and subtractability, which determines the extent
to which the beneﬁts consumed by one individual subtract from the beneﬁts available to others. El
CPR in this article is classiﬁed as subtractable, as appropriation from the common pool is disadvan-
tageous to the good of the collective, but not exclusive, as all players may make appropriations,
irrespective of permission.

A side effect of a common pool is that each player trying to satisfy themselves maximally may
conﬂict with the collective goal of sustainability of both the resource and the players. Por lo tanto
the players need to be satisﬁced (satisﬁed minimally) at least to some degree (con el tiempo); sin embargo,
attempting to satisfy all the players maximally may deplete the resource.

The dilemma hence becomes a matter of personal security, with players having to evaluate the
corto- and long-term impacts of either saving resources to maximize a private pool or contributing
to a global pot. Whereas the former is the rational short-term action for a reasonable, self-interested
player, the latter creates the “safety net” of an accessible resource, should the players ﬁnd themselves
with a depleted private pool at some point in the future. This yields that the pool is sufﬁcient to
satisﬁce needs if the players manage to cooperate; sin embargo, there is simply not enough if they fail
to do so.

This provides players with a set of possible strategies for playing the game. Individual utility of
a player is maximized by withholding provision of their own resources on the assumption that all
other players contribute fully (the Nash equilibrium); but a player can also demand the maximum
appropriation irrespective of their actual need and can also cheat on the appropriation of resources.
This prompts the need for conventional (institutional) rules to regulate behavior but also observa-
tional, sanctioning, and dispute-resolution mechanisms to check for and punish noncompliance (cf.
Pitt, 2021, capítulo 5).

For this system, we take N players i ∈ {1, . . . , norte} that perform the following actions in each
iterated round t ∈ {1, . . . , ∞}: (a) makes a provision of resources due to sanctioning, si; (b) makes a
provision of resources through tax, de; (C) makes a demand for resources, di; (d) receives an allocation
of resources, ai; (mi) makes an appropriation of resources, a (cid:4)
i; y (F) receives a salary for roles in
government gi. The total resources accrued at the end of a round is hence the utility of a player and
is given by

ucpr
i

= a

(cid:4)
i

+ gi − (si + de)

(4)

2.3.3 Collective Risk Dilemma
By creating a common pool of resources, there is a facility to mitigate a disaster (a catastrophic event
eso, if unmitigated, has the power to inﬂict great damage across the multiagent system), so long as
a threshold is reached. This converts a simple Linear Public Goods (LPG) game into a twofold
problem known as the Collective Risk Dilemma (CRD).

This dilemma, a subset of games known as threshold public goods games (Cadsby & Maynes, 1999),
provides N players with T rounds to reach a ﬁxed threshold. In the event of reaching this threshold,
the individual damages incurred in the event of disaster can be mitigated to reduce the effect, pro-
viding a collective beneﬁt in the form of an increased likelihood of survival. Por último, the CRD
aims to conﬂict the individual, short-term beneﬁt of resource retention with the collective, long-term
beneﬁt of disaster mitigation. Rationally, self-interested behavior dissuades contribution to a com-
mon pool; sin embargo, this would be detrimental to the collective, as having all members contribute
is the optimal strategy when the resource loss incurred from unsuccessful mitigation outweighs any
short-term beneﬁt.

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In this article, we increase the difﬁculty of the CRD by varying the uncertainty of the system—we
consider the need for external self-organization when ﬁrst the threshold value that needs to be
reached and second the knowledge of the periodicity of disaster are visible or hidden. Este último
gives rise to the notion of timing uncertainty stipulated by Domingos et al. (2020), who identify that
in real-world scenarios, the quantity needed to contribute and the time when it must be achieved
are often not certain and instead based on predictions.

We model the expected utility for each player i ∈ {1, . . . , norte} as dependent on the total resources
in the common pool R, the threshold needed to mitigate disaster TH, the geographical position of
the player pi, and the magnitude of the disaster M. The resulting utility is hence

(cid:2)

ucrd
i

if R ≥ TH
0
−U(pi, METRO, R) de lo contrario

where the utility mapping U(pi, METRO, R) is speciﬁed in section 4.1.

(5)

2.3.4 Total Utility Gain
Through engaging in the three games detailed earlier, each player i ∈ {1, . . . , norte} gains a total utility
per turn u∗

i , as computed by Equation 6:

∗
tu
i

= ush
i

+ ucpr
i

+ ucrd
i

(6)

Note that each of these three operational-choice resource-competition games has a Nash equilib-
rium solution that operates to the detriment of the others. This solution concept in one game has an
adverse knock-on effect on another; therefore the Nash equilibrium is no guarantor of cooperative
survival in this context. Note that removing any game would remove the element of social con-
struction that impacts decision-making in the others. Simply offering players an endowment would
remove the need for social coordination, and removing any of the two dilemmas would trivialize the
problema: The lack of a CRD means that all resources exist in a closed system, which simpliﬁes the
resource management problem. En cambio, we introduce self-organizing mechanisms that effectively
create three social-choice political-competition games that socially construct resources (institutions,
social capital, etc.) that have side effects (change the constraints) on the operational-choice games
(but that is not to say that the social-choice games cannot be “gamed” either, p.ej., by autocratic
takeover of governance).

2.4 Self-Organizing Mechanisms
The games introduced in the previous section introduce various social dilemmas. Por ejemplo, el
stag hunt game presents players with a dilemma of risk minimization versus reward optimization.
The CPR situation is essentially a problem of short-term response escalation leading to long-term
ruination, eso es, el (supposedly inevitable) tragedy of the commons. Both the CPR and CRD
games present an issue of free riding: The optimal strategy is not to contribute and to rely on every-
one else providing enough, which works ﬁne for one practicing it—provided there is only one. Si
everyone adopts this strategy, there is disaster for all. To overcome these problems or avoid socially
suboptimal outcomes, various mechanisms have emerged based on self-organization through the
social construction (Berger & Luckmann, 1966) of rules, relaciones, and reputations.

2.4.1 Gobernancia
The social construction of rules to help resolve a social dilemma or collective action problem has
been a key tool to help communities solve political problems, such as those identiﬁed by Plato in

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The Republic, Por ejemplo, how to prepare the “best suited” to rule for the common good and to
prevent those ill suited to the task from occupying political ofﬁce.

Después, Aristotle wrote of developing a paradigm of constitutional self-government, com-
bining both “aristocratic” and “democratic” elements (Durant, 2006). This approach to governance
gave rise to the classical Athenian political regime of democracy, in which the citizens can be char-
acterized as collective rulers, delegating governmental duties according to a system of votes, incluido
sortition (the selection of public ofﬁcials by random sampling from a larger population). In classical
Athenian terms, this represented ruling, as citizens, and being ruled over, by other citizens, in turns.
Sin embargo, the ongoing development of the principles and practice of democratic self-governance
through history can be viewed as a gradual evolution along a continuous spectrum into a better
forma, or evolution as a series of punctuated equilibrium states, akin to regular “software updates”
(Manville & Ober, 2019). Either way, aunque, the social construction of sets of rules—that is, el
mutual agreement of conventional rules which serve to regulate or constrain behavior—is not the
sole preserve of city-states or national governments.

En particular, Ostrom’s extensive ﬁeldwork collected rigorous empirical evidence to demon-
strate how communities, throughout history and geography, could develop a long-lasting solution
to a collective-action problem involving sustainable CPR management based on the formation of
self-governing institutions (Ostrom, 1990). Además, these communities were able to coordinate
their activities with others to solve such problems at scale in a system of systems (see also Lansing
& Kremer, 1993). The common features of Ostrom’s self-governing institutions can be expressed
as design principles, and the principles themselves have been reexpressed algorithmically for use in
electronic institutions (Pitt, 2021).

La necesidad de, and beneﬁt of, some form of governance as a mechanism for self-organization is
further demonstrated by the codiﬁcation of rules of order for deliberative assemblies (Robert et al.,
2000). These rules are applicable from parish councils to national parliaments, and this work pro-
vides a standard handbook documenting best practice in all such situations. Sin embargo, many other
situations are also covered by socially constructed rules, from contracts of employment through
terms and conditions of service up to international treaties and the rule of law.

2.4.2 Trading
A second form of self-organization, providing the wherewithal to relax the constraints of these
juegos, is the social construction of conceptual relations, Por ejemplo, though interactions that create
externalities. In economics, generally speaking, externalities are beneﬁts that accrue to a third party as
a result of interaction between two other parties; sin embargo, successful interactions can also provide
externalities that beneﬁt both parties, Por ejemplo, creating trust relationships (which can also be
reported to the beneﬁt of other parties). These externalities have been called social capital (Putnam,
2000), but because of the connotations associated with that term, the term we use here is conceptual
resources (es decir., these are abstract, socially constructed resources in the “minds” of the agents, no
physical resources like ﬁsh or deer).

Por ejemplo, Malinowksi’s (1920) anthropological research studying the Kula ring exchange
system in the Trobriand Islands demonstrated how trading established cohesive bonds between
otherwise disparate groups. The Kula ring spanned 18 island nations across the Massim archipelago
of Papua New Guinea and involved thousands of participants.1 All Kula valuables are handmade
trinkets that are traded solely for the purpose of currying favor in the archipelago and boosting an
island’s social prestige. So, an islander would make an arduous journey by canoe to present a gift to
a (higher-ranked) person on another island. Sin embargo, it was considered a social faux pas to retain a
Kula gift, and so the second person would make an arduous journey by canoe to present the gift to
yet another person on a third island. This would be repeated, forming a ring around the islands. El

1 In passing, it is Malinowski’s (1920) description of the Kula ring that inspired the archipelago as the basis for the scenario used in

this article.

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system of continuous trade resulted in a form of “gift economy” whose crucial feature was to create
reciprocal relationships so that in times of hardship, one island would be incentivized to support
otro.

In this way, trading creates a deeper context that essentially affects motivations, decisiones, y
behaviors in social dilemmas. The giving of gifts, of different value and frequency, serves to create
an economy of esteem (Brennan & Pettit, 2005). The crucial feature of “esteem” is that it cannot be
traded—it can only be produced—but it can have a signiﬁcant effect in free markets and other
social dilemmas. Por ejemplo, it has been shown in an iterated time-slot scheduling system that
exchanges based on the production and calling in of “favors” enabled a completely decentralized
system with no central authority to approximate the optimal solution. Any differences were offset by
the lower cost of the increases in communication compared to the cost of computing that optimal
solución (Pitt et al., 2014). De hecho, many problems of collective action and knowledge management
rely on lowering transaction costs, by grafting the prosocial behaviors (p.ej., giving gifts or doing
favors) onto actions that people would have done anyway (Ober, 2017).

2.4.3 Forecasting
Instances of forecasting or divination, more or less scientiﬁcally, to support or guide decision-
making can also be seen throughout history. Por ejemplo, in classical Greece, oracles were suppos-
edly gifted people who were thought to be able to channel inspiration from the deities to generate
prophetic predictions of the future. In ancient Delphi, Greece, the Pythia spoke for the oracles of
the god of the sun and light, Apollo. She responded to the questions of people from all walks of
vida, whether citizens or kings, on diverse issues ranging from political impact and war to laws and
personal issues (Broad, 2007). En general, the Pythia was regarded as the highest civil and religious
authority, inﬂuencing both the government’s and individuals’ decisions on all important topics.

Sin embargo, soothsayers, shamans, witch doctors, priests, etcétera, have all claimed some form
of divine insight for predicting the future. Por ejemplo, during the 17th century, plague doctors
began to prevail as a means of forecasting treatment for the Great Plague of London. They were
hired by cities to treat plagued patients from all backgrounds, though they rarely succeeded, serving
instead to record death tolls and the number of infections (Byrne, 2006). De nuevo, these plague doctors
would serve as the local authority on medical treatment, helping inﬂuence the government on which
methods were effective at the time. Although such activity took place before the germ theory of
disease was properly articulated, it can be seen as the forerunner to statistical epidemiology, cual
uses rather more informed theories and techniques to help formulate public health policy.

Feedback is a critical feature of forecasting, and in economics, scoring rules have been proposed
that give credit (or otherwise) to forecasters for the accuracy (or lack of it) of their predictions
(Harrison et al., 2017). One of the particular problems with forecasting, aunque, is that predictions
can affect behaviors that give rise to different outcomes. Por ejemplo, a weather forecast for rain
may inﬂuence someone to carry an umbrella; it would be inappropriate to accuse the forecaster of
being incompetent because they did not get wet.

2.5 Summary: The Challenge of Cooperative Survival
In this context, the challenge to ALife becomes not just a matter of life but a matter of life and
death: Which combination of what form of these self-organizing mechanisms “solves,” optimally
or otherwise, the cooperative survival game under what dimensions of scale, incertidumbre, y estafa-
straints of the subgame. In the next section, we design a self-organizing multiagent simulator to
address this challenge.

3 System Design

This section details the codiﬁcation of the overall “platform” for this multiagent system. Tal como,
we discuss the sequence of actions that drive this simulator in section 3.1 by presenting it as a

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state machine, followed by a discussion of the agent architecture in section 3.2 and how agents may
interact with the different self-organizing mechanisms. We conclude this section by discussing the
representation of rules for the governance mechanism in section 3.3.

3.1 Simulator Design
We implement an iterative simulation in which all islands in the archipelago play up to three political
metagames each turn. The simulation is structured as series of seasons and turns, which conclude
once all the islands “die.” The objective for the islands is to survive for as many turns and seasons
as possible. We set up our simulation such that agents will play the games for 50 días, with disasters
affecting the archipelago every 5 días. This yields 10 seasons of play.

A turn is deﬁned as a series of exchanges between agents in which islands receive resource up-
fechas, attend Inter-Island Organization meetings (see later), and interact with one another and the
game state through actions. A turn can be broken down as follows:

1. Resource updates are given for each island and on the global game state.

2. The Inter-Island Governmental Organization (IIGO) decides rule changes, elecciones, y

sanciones.

3. The Inter-Island Forecasting Organization (IIFO) provides a forum for information

exchange to mitigate both short- and long-term risk dilemmas.

4. The Inter-Island Trade Organization (IITO) facilitates gift exchanges and allows agents to

communicate to make deals between one another without organization supervision.

5. Islands submit decisions on their actions to the server to formally end the turn.

6. A check is made to see if a disaster occurs this turn.

7. The server processes actions and updates game and island states:

a. A cost of living is subtracted from an island’s pool before the next term. This is the
simulation-level equivalent to using resources to stay alive (p.ej., food consumed).
These resources are permanently consumed and do not go into the common pool.
Note that this is not the same as the tax.

b. Check if the game is over.

C. Check if any islands are critical (es decir., below the threshold).

d. Check if any islands are dead.

Además, a season is deﬁned as a series of turns and concludes with a disaster. Seasons formalize
the ﬂow of the game and provide a method to track the number of disasters the islands survive. Nosotros
illustrate our formal deﬁnition of a turn in Figure 3.

3.2 Agent Design
All agents i ∈ A are implemented as a data structure such that all agents contain sufﬁcient parame-
terization to participate in the various metagames g ∈ G, resulting in I = < A, G >.

Each agent must have the capacity to (a) identify other agents and (b) interact with the
self-organizing mechanisms of forecasting, gifting, and governance. Agents are ascribed a unique ID,
represented by an integer from 1 to the total number of agents, that remains constant throughout
the entire simulator.

For interfacing with the IIGO, a global rule cache stores the rules that are available to the IIGO,
and a local rule cache stores those that are in play. The representation for these rules are later
discussed in section 3.3. Agents also maintain knowledge of the agents that hold power in the
IIGO, as this process is not anonymous.

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Cifra 3. Visualization of a turn. IITO = Inter-Island Trade Organization; IIGO = Inter-Island Governmental Organiza-
ción; IIFO = Inter-Island Forecasting Organization.

Además, for interaction with the IIFO, agents make a disasterPrediction, as shown in Table 1.
This stores predictions concerning the position, magnitude, and periodicity of disaster, así como
the conﬁdence that the agent has in its prediction.

Finalmente, to engage in the IITO, agents must ﬁrst engage in opinion formation. Mesa 2 demon-
strates the variables that are required for this: An agent’s decision to report resources must be
tracked to inform their trustworthiness, as shown in the variable AgentReportedResources. This maps
each agent’s ID to a Boolean corresponding to whether an agent has reported their resources on
that turn. Además, the gifts that have been received from other agents affect the quality of gifts
that an agent will, Sucesivamente, offer. This is recorded in the ReceivedOffer variable, which again tracks the
mapping of agent IDs to numerical gifts.

Además, throughout the simulator, the opinions that agents have of one another ﬂuctu-
ate based on gifting and lawful behavior. This is tracked in the variable AgentOpinion, donde el
agent ID is mapped to a numerical “score,” deﬁned on [−maxOpinion, maxOpinion], with larger, posición-
itive values corresponding to a higher opinion (parameterization is discussed in section 4.2.2). El
range of possible opinion values is constrained such that it is not possible for successive negative
interactions to cause opinion to “spiral out of control.” This effectively gives agents the opportu-
nity for “redemption” (o, contrarily, it means that they cannot act kindly in the early stages of the
game in order to act tyranically later on, while still reaping the rewards of a high trust value).

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Mesa 1. Parameters held in the disasterPrediction data structure.

Parameter

Coordinate X

Coordinate Y

Magnitude

Conﬁdence

Threshold

Período

Mesa 2. Parameters held in the Agent data structure.

Parameter

AgentReportedResources

ReceivedOffer

AgentOpinion

Range

N ∈ [0, 10]

N ∈ (0, ]

N ∈ (0, 1]

norte

Range

map{A, Bool}

map{A, norte}

3.3 Rule Representation
Rule generation represents a large portion of the function of the governmental organization. Para
this simulation, we represent our rules as a set of vectors such that the principles of linear algebra
can be applied. The premise of this choice was such that, if a rule could be represented by matrices,
then agents could look up every element of the matrix with minimal complexity.

Following is an example of this matrix-based rule representation:

Regla 1. If you are expected to pay x amount of tax, the amount of tax you pay must be x.

If our goal is simply to ensure that an agent pays the expected amount of tax, a basic mathematical
operation we can perform is to subtract the actual tax paid from the expected. If we obtain 0 de
this subtraction, we can conclude that this agent has adhered to this rule. Formalmente, letting x and y
represent the expected and the actual paid amount of tax, respectivamente, we calculate the following:

y − x = 0

To turn Equation 7 into a matrix calculation, we introduce some trivial coefﬁcients:

−1 ∗ x + 1 ∗ y = 0

Ahora, we can write Equation 8 as a matrix calculation:

(cid:5)

(cid:6)

−1 1

(cid:7)

(cid:8)

X
y

= 0

(7)

(8)

(9)

Following is a more complicated example:

Regla 2. If you are expected to pay x amount of tax, the amount of tax you pay must be at least x.

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Mesa 3. Auxiliary codes for rule encoding.

Auxiliary code

Significado

= 0

< 0 ≥ 0 != 0 real We can rewrite the matrix equation as an inequality: (cid:6) (cid:5) −1 1 (cid:7) (cid:8) x y ≥ 0 (10) The addition of the “at least” (i.e., ≥) in Equation 10 adds complexity to the proposed matrix scheme. For this reason, it is not possible simply to check for equality, and although all calculations are compared to 0, further encoding is needed to see how the comparison is made. To achieve this, we incorporate an auxiliary vector containing a list of comparison codes, as seen in Table 3. However, with this approach, problems are still encountered with a rule like Rule 3. Rule 3. If you are expected to pay x amount of tax, the amount of tax you pay must be at least x + 5. To capture such cases of rules, we introduce a constant to the input list, as in Equation 11: (cid:5) −1 1 −5 ⎤ ⎦ ≥ 0 ⎡ ⎣ (cid:6) x y 1 (11) This now allows the encoding to capture any linear equation or inequality with any constant shift. It is important to note that the dimensions of this input vector can be arbitrarily large, as for each additional constraint a rule has (and a variable needed to ﬁll), we expand the input dimensions of our vector. 4 Self-Organizing Mechanisms and Games This section discusses the methods for codifying the aforementioned self-organizing mechanisms and games by specifying the algorithms. 4.1 Disaster All agents are distributed across a 2-D plane ranging from (0, 0) to (10, 10). For simplicity, the common pool is interpreted to have a presence outside the realm of the games such that the damage dealt to the common pool is independent of the location of the disaster. Naturally, a well-maintained common pool will allow for the maximum mitigation of damage from the disaster (the resources held by the agents will minimally deplete), incentivizing the agents to self-organize for cooperative survival. The disaster generates uniformly across the 2-D plane as a point and damages the agents accord- ing to two “effects”: The soloEffect is calculated according to the magnitude of the disaster divided Artiﬁcial Life Volume 29, Number 2 211 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u a r t l / / l a r t i c e - p d f / / / / 2 9 2 1 9 8 2 1 3 0 4 3 5 a r t l / _ a _ 0 0 4 0 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 M. Scott and J. Pitt Mechanisms for Cooperative Survival l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u a r t l / / l a r t i c e - p d f / / / / 2 9 2 1 9 8 2 1 3 0 4 3 5 a r t l / _ a _ 0 0 4 0 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 4. Algorithm 1: resource deduction due to disaster. by the squared distance to each agent, which is subsequently converted to a propEffect by taking the ratio of the soloEffect to the total damage felt across all agents. Disaster mitigation is achieved depending on the common-pool threshold, thresholdCP, and the resources available in the common pool, currentCP (TH and R, respectively, in Equation 5). The resource deduction to the agents, agentResources, and common pool is then calculated according to Algorithm 1 (Figure 4). In this algorithm, if the resources in the common pool are above threshold, the impact is halved for all agents. This incentivizes ﬁlling the common pool to at least the baseline, as the total damage can be somewhat mitigated. Following this, the resources in the common pool are compared with the aforementioned impact, where if the resource availability exceeds the impact, the damage taken is 0. This incentivizes overﬁlling the pool. Ultimately, this algorithm rewards both a minimal ﬁlling of the pool and an overﬁlling, thus encouraging self-organization. 4.2 Trading Trading serves as the main self-organizing mechanism for facilitating opinion formation over the social network, which in turn inﬂuences the electoral process for introducing politics to the multi- agent system. We break down the process of gifting into two main stages: sending gifts and receiv- ing gifts. 4.2.1 Requesting Gifts Each client has the capacity to make a gift request. We model the gifting system as a set of re- quests made by the agents, based on their private pool of resources. If an agent is below the critical 212 Artiﬁcial Life Volume 29, Number 2 M. Scott and J. Pitt Mechanisms for Cooperative Survival threshold, they will ask all other agents for a gift equal to three times the cost of living. Alterna- tively, an agent will have a 40% chance of asking each other agent for a gift equal to the following: ReceivedOffer[ agent] = 2 ∗ (AgentOpinion[ agent] + costOfLiving) (12) 4.2.2 Receiving Gifts Gift response sessions are handled such that all requests are seen at the same time, by passing a list of gift requests to each agent. Upon receiving this list, the agent will sort the requests made by descending opinion, allowing for agents to prioritize their favored other agents. After sorting, one of three possible responses is made: 1. An agent will respond with a gift of 0 in three cases: either if (a) the private resources held by the agent are less than the anxiety threshold (250, for this article), (b) the current (private) resources held by the agent are less than the request being made, or (c) the opinion held of the agent making the request is less than 0. 2. If not responding with a gift of 0, an agent will respond with a gift equal to the request in two cases: (a) the opinion held of the agent making the request is equal to the maxOpinion (30, in this case) or (b) the agent making the request has resources below the critical level. 3. If neither of these two cases passes, the default gift request is handled as follows: (cid:13) response[agent] = min ReceivedOffer[agent] , (cid:14) currentResources2 100 ∗ anxietyThreshold (13) 4.2.3 Opinion Formation It is the process of receiving and proposing gifts that permits agents to develop opinions of the other agents and, by extension, form a social network in the simulator. The magnitude of change in the opinion held of an agent during trade is based on the response received to a proposed gift request. If the response to the request is nonzero but less than the requested amount, the opinion held of the responding agent increases by a single point. If instead, however, the response is greater than the request, the opinion held of the responding agent increases by 20% of maxOpinion. Furthermore, if the agent proposing the gift request is in a critical state (that is, has resources below the critical value) and receives a nonzero response, the opinion held of the responding agent increases by 50% of the maxOpinion. In any case, additional generosity is encouraged, as it facilitates a faster development of positive opinion. Finally, if the received amount is zero, then the opinion held of the responding agent decreases by a single point. If all of these cases fail, the default strategy is not to update the opinion at all. 4.3 Governance Deﬁning social choice political metagames to regulate behavior in operational-choice resource- competition games requires collective self-governance, and this self-organizing mechanism requires conventional rules (institutions; Ostrom, 1990) and methods to select, revise, apply, revoke, and enforce those rules. Given that agents are assumed to be essentially equal (in territory, mineral resources, person power, technological development, etc.), we follow Ober’s Demopolis thought experiment (Ober, 2017; Pitt & Ober, 2018). There are two points to note about governance: structure and representation. First, regard- ing structure, following the “standard” (and typically ascribed to Montesquieu) blueprint for the Artiﬁcial Life Volume 29, Number 2 213 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u a r t l / / l a r t i c e - p d f / / / / 2 9 2 1 9 8 2 1 3 0 4 3 5 a r t l / _ a _ 0 0 4 0 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 M. Scott and J. Pitt Mechanisms for Cooperative Survival separation of powers and checks on the use of those powers, government in the archipelago is represented by three distinct institutions: the legislative institution, which makes rules; the executive in- stitution, which applies rules; and the judicial institution, which interprets rules. Second, regarding the representation of those separated powers, we follow the standard rep- resentation in norm-governed multiagent systems with institutional facts (Artikis et al., 2009) to distinguish between institutionalized power (as opposed to physical actions) (Jones & Sergot, 1993), permission, and obligation. Institutionalized power is the performance of a designated act (typically but not necessarily a speech act) by an assigned agent occupying a speciﬁc role, which “counts as” an institutional fact be- ing (mutually agreed) to be true. Then, institutionalized power in the three government institutions is assigned to those agents occupying roles of Speaker in the legislature, President in the executive, and Judge in the judiciary. By performing designated actions, some of which are permitted (sometimes, but not always, power implies permission) and some of which are obliged, an agent occupying a role sees to it that certain institutional facts are true, as discussed in the subsequent sections. Note that as actions are sequential, we can use the current state to compute what power, permissions, and obligations apply to an agent in that state, without using the Event Calculus, for example (Artikis et al., 2015). 4.3.1 Roles and Powers To help distinguish between institutionalized power and physical capability and between (institu- tional or physical) power and permission, consider the role of Judge. Only the agent occupying the role of Judge can declare that an audit of another agent is to be carried out: Any other agent making such a declaration is merely making noise. The Judge is permitted to conduct an audit, which is a physical action, but only if an audit has been declared. Only the agent in the role of Judge can declare the result of an audit; moreover, an agent is not permitted to declare the result of an audit of itself (reﬂecting the principle of nemo judex in causa sua, that no one should be a judge in their own case). In addition, the agent in the role of Judge is empowered to impose sanctions, but is only permit- ted to impose sanctions if the audit has revealed a breach of the rules—in this case, power does not imply permission. Note that if the Judge agent does impose a sanction without permission, the institutional fact that there is a sanction is still true; it is the Judge agent that has violated the norma- tive rules. For this reason, there should be an appeals procedure (Ostrom, 1990), but for simplicity, in this system, agents are effectively regimented (Jones & Sergot, 1993) and cannot do what is not permitted. The agent occupying the role of President is empowered primarily to do three things: to set the level of taxation, to declare the allocation of resources, and to set the agenda for the legislature. Note that only the agent occupying this role can make declarations that count as determining the tax level, the resource allocation, or the agenda: Any other agent making such actions is again making noise. Similarly, the powers of the agent occupying the role of Speaker are primarily associated with the conduct of elections and the declaration of results. Only the agent in the role of Speaker is empowered to declare the result of a vote, and so only then does a rule become active, revised, or revoked. Note that there are also obligations associated with this role, most importantly, that the Speaker is obliged to select at least one rule for voting if rules have been selected by the President and that the Speaker is obliged to declare results according to the way votes were cast (cf. Pitt et al., 2006). 4.3.2 Voting Proceedings in the governmental organization are based on a simple voting system, where all agents will compile a ballot for the topic in hand to be sent to the Speaker for broadcasting. Voting oc- curs in two instances: When choosing to implement a new rule and when appointing the new roles in government. All agents are programmed to vote in favor of a proposed rule. When voting on elections, however, the agents implement a Borda count method, where N agents are ranked from 214 Artiﬁcial Life Volume 29, Number 2 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u a r t l / / l a r t i c e - p d f / / / / 2 9 2 1 9 8 2 1 3 0 4 3 5 a r t l / _ a _ 0 0 4 0 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 M. Scott and J. Pitt Mechanisms for Cooperative Survival highest opinion to lowest opinion. The Borda score for each agent a is then computed by Equation 14, where b represents the number of ballots: b(cid:4) i=1 N − rank(a, vi) + 1 (14) where rank(a, vi) is the position (rank) of agent a in the ballot vi of agent i. 4.3.3 Taxation Governance serves as a self-organizing method for replenishment of the common pool. We take the agent currently elected as President for deﬁning taxation, where a percentage of all agents’ resources are taken each turn. Depending on the availability of the forecasting organization, this taxation can be either informed (based on previous assessment of the common pool) or random (assuming that the forecasting organization is deactivated). Uncertainty is introduced to the system in two ways—through stochastic period and magnitude: Disasters can occur regularly, with a known interval period, or randomly, obeying a geometric distri- bution such that the expected period is the ﬁxed period of the regular case and variably visible common pools—agents may or may not have knowledge of the common pool’s threshold. The strategy for taxation is hence dependent on the uncertainty of the system and a set of tuning parameters that deﬁne the numerical contribution needed with respect to the games. The ability to use the forecasting organization is not always available, hence the elected President of the IIGO makes a prediction for the period of disaster and the common-pool threshold on both the ﬁrst turn of the game and any subsequent turns when a disaster occurs. This guess is randomized from [2, 10] for the disaster periodicity and from [200, 1000] for the threshold. Naturally, this is an inferior strategy to using the forecasting organization, as both of these guesses run a severe risk of overestimation, meaning that the common pool will either not be ﬁlled in time or heavily overcontributed to, resulting in wasted utility. The general principle for taxation is to predict either of these quantities on each turn, CPT (cid:4) t t, whether they be visible, estimated by the President, or estimated by the forecasting organiza- and T (cid:4) tion, giving the “quality” of taxation as known > forecast > President.

Simply, if a quantity is known, then its prediction is equal to the ground truth. If a quantity
is hidden, then its prediction will be equal to the guess made by the forecasting organization in
sección 4.4.1, if active, or else the President.

The total required contribution per agent per turn ci,t with i ∈ {1, . . . , norte} is ultimately deﬁned in
Ecuación 15, with Nt representing the number of alive agents and CPt the resources in the common
pool on turn t. The overﬁllRate represents the “multiplier” applied to the common-pool threshold
to request agents to contribute resources surplus to the minimum threshold,

(CPT (cid:4)
t

ci,t=

∗ overﬁllRate) − CPt

Nt ∗ T (cid:4)
t

(15)

to represent that the taxation per turn should be split evenly across all alive agents and all turns
leading up to the next disaster.

4.3.4 Sanctioning
Sanctions are interpreted as a ﬁne imposed on any agents who break a rule during the simulation
run time.

Sanctions are assigned based on ﬁve increasing tiers of severity 1–5. A sanction tier is allocated
based on the running total of rules broken by an agent, with the thresholds deﬁned as 1, 5, 10, 20,
y 30, respectivamente.

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The sanction tier deﬁnes the severity of ﬁne imposed on the agent. This payment must be made
directly to the common pool, as avoidance will result in further sanctions being applied. The sanction
requirements for the tiers increase with severity and are numerically represented by a base cost of 10
resources, plus a fraction of the current resources. Increasing from Tier 1 to Tier 5, the additional
fractions are 0%, 20%, 30%, 50%, y 80%, respectivamente.

4.3.5 Order of Proceedings
The overall process for governance follows a linear path. Upon initiating the governmental organiza-
tion at the start of a turn, events proceed such that the Judge will evaluate previous performances, el
President will take appropriate action to deal with the Judge’s ﬁndings, and the Speaker will announce
the actions carried out by the President.

The governmental organization has a strict order of proceedings, como sigue, with all branches

working in tandem.

4.3.5.1 Initial Proceedings
At the start of each turn, the payment made to each governmental
branch from the common pool is increased if agents have voted to increase the respective budget.
Following this, any agent occupying a role of power has the counter tracking their total duration
spent in power incremented by 1.

4.3.5.2 Judicial Branch
The Judge begins by selecting an agent in the system and inspecting
their decision history (such as tax contributions) to evaluate if the agent has complied with the rules
throughout the simulation. Following this, the Judge is able to deﬁne the severity of the sanction
needed and to apply it accordingly. En tono rimbombante, the Judge will not take their own previous actions
into consideration, making them exempt from sanctioning.

4.3.5.3 Executive Branch
The agent occupying this branch begins by compiling a report
concerning what each agent (a) possesses and (b) claims to possess in its private pool. This is then
passed to the Judge to reevaluate if an agent should be pardoned. En tono rimbombante, if an agent refuses to
report their current resources, the shared opinion of this agent decreases by one stage (sección 4.2.3),
under the assumption that if an agent refuses to report their resources, the agent is unlikely to pay
tax as well. Following from this, the President broadcasts the amount of tax needed to be paid by
each agent, according to Equation 15. This serves as the key mechanic for developing the resources
in the common pool.

The President also facilitates allocations from the common pool, as well as taxation. Resource
redistribution from the common pool occurs if a request is made, where agents will ask for an
allocation if they have 300 resources or fewer, making a request for an allocation of 50 resources.
The allocation is calculated based on the total request made by all agents. If the total request is less
than 75% of the common pool, the individual requests are granted without question. If this is not
the case, the allocation to agent i on turn t is granted according to Equation 16:

allocationi,t = requesti

∗ CPt ∗

3
4 ∗ totalRequestt

(16)

Finalmente, all agents in the system are polled for a new rule that they wish to be implemented in
gobierno. The President selects at random a rule from this list to be supplied to the Speaker for
broadcasting to all agents.

Legislative Branch

4.3.5.4
Concluding the governmental proceedings is the legislative
branch. Upon broadcasting the newly proposed rule, all agents will cast their votes to offer a deci-
sion to accept or decline the rule. This decision will hence inform if the new rule is added to the

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list of active rules. All agents will then vote on who they want to act in government, according to
Ecuación 14. This result is then announced by the Speaker.

4.4 Forecasting

4.4.1 Disaster Mitigation
When the common-pool threshold is invisible, self-organization through forecasting serves as a
means of helping counteract the increased uncertainty imposed on the multiagent system. Cuando
forecasting is active, agents will make regular guesses at the value of the common-pool threshold
and the period of disaster based on the damage that they have received. If the damage taken is too
alto (>200), agents will increase their estimate of the common-pool threshold, hoping to further
mitigate the damage taken. En cambio, if the agents seem to be taking little to no damage from the
disaster, they will decrease their estimate of the common pool to reduce the resources lost from
taxation. Both of the updates to this prediction are randomized in the range [50, 100]. The disaster
period is estimated by averaging the periods of all previous disasters.

In the event that a disaster is yet to have occurred, the predictions are initialized with the
common-pool estimation in the range [0, 1000] and the disaster period equal to the ﬁrst turn on
which it occurs.

Following a forecasting session, the ﬁnal predictions made are averaged evenly across all agents,
offering a “wisdom of the crowds” approach (Surowiecki, 2004), as an average of the guesses of all
agents is more powerful than any individual guess.

4.4.2 Improving Foraging
Forecasting, furthermore, helps with the quality of foraging. In each forecasting session, agents
selectively broadcast the previous foraging choice that they made to other agents. When this mech-
anism is active, information is given about the natures of the other agents, allowing inferences to
be made about if the deer population is becoming over foraged. This ultimately has the effect of
helping reduce the risk of hunting deer to extinction.

4.5 Stag Hunt and Foraging Returns
We codify the conventional stag hunt dilemma such that all agents have no a priori knowledge
of the other agents’ decisions, using only their interpretations of the population sizes shared
by the forecasting organization. Three foraging types are conditionally implemented based on the
ambiente:

randomForage. We introduce an equiprobable chance of either foraging a deer or choosing to ﬁsh.
This forage type is chosen for the ﬁrst ﬁve turns to build up knowledge of the randomized
initial population or if forecasting is disabled.

desperateForage. In the instance that an agent has a critical level of resources, they constantly forage
deer, hoping that another agent has made the same decision, hence looking for the highest
possible payoff.

ﬂipForage. Agents forage the opposite of what the mass did the previous turn and forage deer with
an input amount inversely proportional to the sum of contributed resources. This foraging
method is chosen as the default, assuming the criteria are not met for the previous two
methods.

This foraging decision also helps deﬁne the input resources, which represents the number of re-
sources an agent contributes to helping fund the expedition: In the instances of either choosing a
randomForage or ﬂipForage, agents will randomly contribute up to 10% of their current total resources,
using a uniformly distributed random variable. When choosing a desperateForage, sin embargo, the agent
makes a last-ditch attempt to generate resources, contributing every remaining resource they have.

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4.5.1 Fish
The utility gained from an individual ﬁsh, F, caught from foraging is modeled on the following normal
distribución:

F ∼ N (1.45, 0.12)

(17)

We assume that, given the sufﬁciently large presence of ﬁsh, the catch rate will always be 100%.

4.5.2 Deer
The utility gained from an individual deer, D, caught from foraging is modeled on the following
exponential distribution:

D ∼ exp(0.5) + 1

(18)

We also propose that deer are harder to catch than ﬁsh, instead having a catch rate of only 80%.
De nuevo, the returns of the deer are modeled in a similar way, proposing a larger output scalar to
incentivize foraging for deer. We also add 1 to the average output of the exponential distribution to
prevent an output of 0.

To model the population dynamics of the system, we impose a rate of reproduction that acts
as a function of the existing deer population. Deﬁning the population per turn pt, el maximo
population size pmax, and the reproduction rate r, we arrive at the population update function

pt = pt−1 + r ∗ (pmax − pt−1)

(19)

using a maximum population size of 20 deer to limit the feasibility of foraging and a reproduction
tasa de 40%.

4.5.3 Utility Tier and Payoff
For both foraging types, it is possible to obtain more than one per expedition—this is henceforth
referred to as the utility tier and is synonymous with the total number of animals foraged per expe-
condición. The utility tier takes the number of resources put into the foraging expedition, junto con
a decayFactor. This decayFactor (0.95 for ﬁsh and 0.9 for deer) aims to replicate the idea that, después
investing resources to reach the foraging location, subsequent animals would be easier to catch, como
no further resources need to be invested for changing location. The maximum possible utility tier
(and hence the maxNumberPerHunt) for this article is 10 for ﬁsh and 5 for deer.

With an inputScalar again keeping the resource investment commensurate with the cost of
living, the utility tier is calculated using Algorithm 2 (Cifra 5), which yields the step function seen
En figura 6.

The resources obtained through foraging are calculated differently, based on the species in ques-
ción. The input resources for each agent are taken as a random fraction of up to 10% of the total
resources. There are two separate distribution strategies: The equal split applies to ﬁshing and is
implemented such that the resources are equally distributed across the number of agents partic-
ipating in ﬁshing; conversely, the proportional split, applied to hunting deer, distributes resources
proportionally to the amount contributed to the hunt. On the basis of the previous sections, nosotros
generate the payoff matrix in Figure 2, with the rewards for foraging as either a deer (D) or a ﬁsh
(F). Naturalmente, there is incentive for both agents to collaborate in the deer hunt so as to reap the
maximal rewards.

4.6 Scaling
We note that the utilities gained from each game are kept within the same order of magnitude
as each other. This ensures that no game is weighted above any other and that all have an equal

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Cifra 5. Algoritmo 2: utility tier.

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Cifra 6. Utility tier visualization for ﬁsh.

impact on the overall system. A key issue with this simulator is that it is possible to set the disaster
threshold so high that the islands are wiped out quickly and the CPR threshold so low that the
islands are essentially indestructible. So we need to ﬁnd a setting that makes survival possible, pero
not certain, so that this system may operate in a “corridor of uncertainty.” Therefore some param-
eters have been experimentally determined to provide a setting in which survival is possible but
not guaranteed, unless the self-organizing mechanisms are used. This provides a “stable” context to
investigate the relationships between independent and dependent variables.

5 Experimental Results

En esta sección, we describe the experimental results of four “survival trials.” After we make a
methodological observation on experimental design for such trials in section 5, each of the four
subsequent subsections explores the performance of the multiagent system under varying degrees

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of uncertainty, numbers of starting islands, and availability of self-organizing mechanisms. The aim
is to investigate, Sucesivamente, the following four hypotheses:

Hypothesis A. A minimum number of starting agents, termed ‘critical mass,’ is required for
the self-organizing mechanisms to have a positive effect (Trials A1–A6).

Hypothesis B. Increasing dimensions of uncertainty and complexity require increasing
opportunity for self-organization (Trials B1–B4).

Hypothesis C. The various self-organizing mechanisms can interact to produce positive
synergies (Trials C1–C4).

Hypothesis D. The various self-organizing mechanisms can interact to produce negative
synergies (Trials D1–D2).

A Python3 program is used to generate the various plots of the survival probabilities in
Figures 7–9. A run is regarded as successful if all agents survive for the entire duration of the simula-
tion and the total quoted survival probability for each pair of agents and active organizations is av-
eraged across N = 30 carreras.

We look at the response to combinations of up to 12 islands with the eight linear combinations of
trading (t) governance (gramo) and forecasting ( F ), representing their activity using the notation t + gramo + F
if all organizations are active. In this vein, a plot point of t + f would represent active trading and
pronóstico, with governance deactivated.

Además, the dimensions of uncertainty are denoted by: t, for a visible disaster period and
CP for a visible common-pool threshold. Por eso, the notation CP + ! T corresponds to a simulation
with both the common-pool threshold visible and time period of disaster not visible.

We also deﬁne a set of parameters that remains constant across all simulations. Each simulation
runs for 50 turns. We ﬁrst model the disaster with a nonstochastic period of T = 5, with magnitude
deﬁned by a Gaussian distribution of mean of 6.5. The resultant damage felt scales this magnitude
por 85. The common-pool threshold needed for the disaster to be mitigated is ﬁxed at 300, con
its initial resources set at 600. For an agent to “die,” they must have at most 200 resources for ﬁve
consecutive turns, starting with an initial 1,000 resources.

All actions carried out by the IIGO yield a cost of two resources, with the exception of broad-
casting taxation. This is done to ensure that taxation can always be carried out despite an empty
common pool, as otherwise, an empty pool can never be reﬁlled. For this simulation, all rules are
instantly put in play to increase the power of the governance organization.

Sección 5.6 contains a summary of the entanglement of games and mechanisms and their interre-
lationships. It also indicates how qualitatively similar the complex scenario studied here is to those
studied in cybernetics. Some of those principles and methods might be useful in further work, para
ejemplo, the concepts of stability (Ashby, 1952) and of a viable system (Beer, 1972), because implic-
itly, one aim of the mechanisms for cooperative survival is to ﬁnd a balance between control and
eficacia.

5.1 Methodology and Experimental Design
Owing to the large number of parameters involved in this simulator,
it is unfeasible to test
all parameter-value combinations using a sweep, Por ejemplo, as all parameters are effectively
unbounded. The methodology for deriving the parameters for the results reported in this section
is based on the mean number of islands seen during experimentation. Parameters are selected to
allow six agents to survive when at least two mechanisms are active and remain constant through-
out the experimentation. Effectively, the parameters are ﬁne-tuned for the case of relatively high
survivability with a mean number of islands and subsequently used for exploring other settings.

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Cifra 7. Survival probabilities for linear combinations of self-organizing mechanisms and starting islands for different
degrees of uncertainty.

En general, when trying to analyze and understand a collective action situation, such as coop-
erative survival, one approach is to make the situation tractable by abstraction, assumption, y
simpliﬁcation. The problem with this approach is that while the situation can then be analyzed
mathematically, it can create specious paradoxes. Por ejemplo, Binmore (2005) likens the appar-
ent paradox of noncooperation inherent to the common formulation of the prisoner’s dilemma
to throwing a strong swimmer into a lake with weights attached to their legs, then neglecting to
mention the weights when claiming that it is paradoxical for strong swimmers to drown in this lake.

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Cifra 8. Survival probabilities for linear combinations of self-organizing mechanisms and degrees of uncertainty for
varying numbers of starting islands. CP = visibility of the common pool threshold; T = visibility of the disaster period;
t = trading; f = forecasting; g = governance.

An alternative approach is to recognize the interconnectedness and interdependence of features
and factors in such situations that, together with randomness, nonlinearity, etcétera, render the
situation resistant to numerical analysis, and to use simulation instead (noting further that com-
plementary approaches can offer different insights into different questions; Powers et al., 2018).
Sin embargo, trying to model the situation, and the agents in their entirety, means building a system
with many parameters with many values, making a full exploration of a huge space by exhaustive
parameter sweep computationally prohibitive, as well as making it much harder to identify and ex-
tract signiﬁcant or meaningful relationships.

Sin embargo, in Just Six Numbers, astronomer Martin Rees (2014) identiﬁes just six physical con-
stants that make for “meaningful” natural science and whose values, if they were only slightly
diferente, would cause the universe to be completely uninteresting, in the sense that neither people
nor planets, stars nor galaxies, would, or even could, existir. There certainly would not be any inter-
esting behaviors, let alone people to propose and test theories about them.

Microworld simulations and experiments, of the kind investigated here, actually have similar
propiedades. There are actually three classes of parameter: “constants,” independent control vari-
ables, and dependent variables. Methodologically, the simulator’s ﬁrst job might be to identify and
ﬁne-tune a set of microworld constants, akin to the physical constants of the “real” universe. Estos
provide sufﬁcient underlying stability, which enables a systematic investigation of the relationship
between the control and dependent variables that enable the simulator to validate, or otherwise, un
experimental hypothesis.

Desafortunadamente,

it can appear that this ﬁne-tuning process involves assigning some perhaps
seemingly arbitrary values to these physical constants, o, worse, cherry-picking results. A pesar de
we would not equate ﬁne-tuning with cherry-picking, we should heed Ostrom’s warning about bas-
ing the formulation of policy on numerical analysis or laboratory studies, which are far removed

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Cifra 9. Survival probabilities for linear combinations of self-organizing mechanisms and starting islands for different
degrees of uncertainty.

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from empirical experience, and we should also avoid ill- or unconsidered formulation of policy
for high-stakes cooperative survival games based solely on these simulation results, under these
condiciones.

5.2 Experiments A: Need for Critical Mass
This set of experiments investigates the importance of a “critical mass” of survivors to facilitate
group survival. We divide the experimentation into four sets, looking at the linear relations between
the proportion of surviving islands and the availability of self-organizing mechanisms for 3, 6, 9,
y 12 initial islands, while in an environment of total certainty (both common-pool threshold and
disaster period are visible).

The results from this line of experimentation show that a threshold number of islands must be
met to have any level of self-organizing mechanisms act favorably. Starting with Figure 7a, Trial A1
shows that any introduction of self-organizing mechanisms performs worse than having none at all.
This illustrates that purely random behaviors (those that are uninﬂuenced by any form of “intelli-
gent” self-organization) outperform the behaviors resulting from the available mechanisms.

This phenomenon can be explained through both the presence of “costly actions” and the de-
mand for taxation. When the IIGO session is run, the various proceedings (such as appointing
roles or proposing rules) have an associated cost that diminishes the common pool. Given the small
mass of islands, very few cooperative metagames can be played, resulting in limited resource gen-
eration. With lessened global utility, the proportion of resources lost due to investment into the
self-organizing mechanisms is far greater than it is with more starting islands.

In addition to this, the algorithm implemented by the IIGO President requires all islands to split
the requirements for ﬁlling the common pool by both the number of islands and the number of days
until disaster strikes. Por esta razón, the daily contribution needed for each island (assuming a desire
to avoid sanctioning) grows exponentially as the number of alive islands decreases. Por esta razón,
we conclude that, given an insufﬁcient starting “mass,” survival is improbable and unassisted by an
introduction of survival mechanisms. We further note that the proportion of survivors is necessarily
inﬂated, given that having even a single island survive represents a high proportion relative to the
other trials.

Trials A2 and A3 (Figure 7b and 7c, respectivamente) show the behaviors of four and ﬁve start-
ing islands. In both cases, there is a neutral impact from greater self-organization, resulting in no
correlation between the proportion of survivors and the activity of the different mechanisms.

When starting with six islands, sin embargo, as in Trial A4 (Figure 7d), we see that there is a drastic
positive impact from having more self-organizing mechanisms active, with this trend continuing
a través de 9 and up to 12 islands in Trials A5 and A6 (Figure 7e and 7f, respectivamente). This conﬁrms
that there is a “critical mass” of islands that must be reached to facilitate a high proportion of sur-
vivors, along with a positive impact from increasing interference from self-organizing mechanisms.
For this situation, we would assert that six islands represents the critical mass of survivors needed
for a feasible system, although this result is not necessarily generalizable.

5.3 Experiments B: Increased Complexity
This second set of experiments aims to illustrate that an increase in uncertainty and complexity
necessitates an increase in the number of opportunities for self-organization. To prove this, we vary
two parameters in the simulator, the visibility of the common-pool threshold and the visibility of
the disaster period, and produce plots showing variations in the number of starting islands, el
availability of self-organizing mechanisms, and the probability of all islands surviving for each case.
An observation that can be made from all four heat maps, irrespective of the level of certainty,
is that for an increasing number of islands, it is near impossible to survive without any organi-
zations active. We propose three possible reasons why a low number of islands may be able to
survive without the ability to self-organize (albeit in very few cases), as shown by Trials B1 and B2
(Figure 8a and 8b, respectivamente).

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Primero, owing to a relatively high initial common pool, because the initial resources in the common
pool stay ﬁxed across all survival trials, a smaller multiagent system means that each agent can take
a larger share of the common pool without completely draining it.

Segundo, because the resource reduction of the common pool is calculated based on the total
damage felt across the multiagent system (es decir., the sum of the damages of each individual agent),
having fewer islands results in a lower overall reduction of resources and helps maintain the size of
the common pool.

Finalmente, the geographical distribution of islands sees them as uniformly distributed points around
a ring. Because we have fewer islands, the average distance between islands increases, significado
that the average distance from each island to the disaster will increase. This again results in less
damage being felt and hence in a lower impact on the common pool. As the number of islands
aumenta, we enter an economy of scarcity: Despite an increase in returns from foraging due to the
increased number of foragers, there are simply not enough self-organizing mechanisms in play to
help redistribute the resources. Having run further diagnostics, sin embargo, the variation from 3 a 12
islands yields an average distance decrease of approximately 20%, which we assert is insigniﬁcant in
comparison to the change in the number of islands.

Considering in detail the role of interdependent mechanisms (over mechanisms in isolation)
with increasing uncertainty, we look at the disparity between the survivability given three active
organizations over the survivability given two or fewer. Having reached the critical mass of islands
established in Experiments A, we have up to a 100% survival chance with three and between 60%
y 80% with just two. Trial B4 shows three transitions in color variation, where a surge from a
10% a 60% a 100% survival rate is achieved by introducing subsequent survival mechanisms.

Supporting this conclusion is the change in color between the number of mechanisms with
respect to the change in uncertainty. Looking at Trial B3 (Figure 8c), we see far greater leaps in
lightness with decreased certainty. Cuantitativamente, with a certainty of “none,” we see that a survival
rate of ≈20% rapidly increases to ≈80%, yielding a 60% increase from two to three mechanisms.
We contrast this with the full-certainty case, in which the increase is from ≈70% to 90%, yielding
a mere 20% increase. This pattern can be seen across graphs for Trials B2–B4 (neglecting the case
below the critical mass) in Figure 8b–8d, from which we conclude that, with increasing uncertainty,
there is a greater reliance on higher levels of interdependence.

5.4 Experiments C: Positive Synergies
This penultimate set of experiments aims to illustrate how, despite the general trend that an in-
creased number of self-organizing methods tends to yield an increase in survivability, the choice
of mechanisms must be carefully considered, and such mechanisms may have to interact in mu-
tually self-reinforcing ways. This set of experiments is visualized with linear combinations of
self-organizing mechanisms and starting islands for different degrees of uncertainty, conseguido por
varying the visibility of the common-pool threshold and disaster period. For the plots in Figure 9,
we denote the visibility of the common-pool threshold and disaster period as CP and T, respectivamente.
The aim of this experiment was to investigate the importance of forecasting and to hypothe-
size that when all disaster parameters are known, this organization offers no additional support
for survival. The ﬁrst contour plot for Trial C1, Figure 9a, shows the instance of complete cer-
tainty when both common-pool threshold and disaster period are known. In this plot, we see that
survival probability is optimized with either all organizations active or simply just the trading and
governance organizations active. The valley caused by the inactivity of governance shows that rules
for taxation and resource management must be in place for the common pool to be regenerated
and appropriately mitigate disaster. Given the situation of having perfect knowledge of disaster
and how to mitigate it (through the common-pool threshold), forecasting offers no beneﬁts to
survivability.

The general trend from Trials C1–C4 (En figura 9, seen from the front [Figure 9a–9d] and from
the side [Figure 9e–9h]) is that the disparity between the survival probabilities of three mecha-
nisms and two mechanisms increases. It can therefore be inferred that increased uncertainty requires

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increased levels of self-organization, as the same level of survivability cannot be achieved between
trials without introducing additional means of self-organization. En tono rimbombante, a perfect 100% sur-
vival rate is feasible across all degrees of uncertainty, so long as there is a sufﬁciently high critical
mass and all three mechanisms are active.

The broader trend from plots for Trials C1–C4 (Figure 9a–9d) indicates that the presence of two
self-organizing mechanisms yields widely varying results, depending on which two mechanisms are
active at any one time. Drawing on Trial C3 speciﬁcally, we can see a disparity between the per-
formances of t + f and g + F, where g + f drastically outperforms the former. This relation demon-
strates that although forecasting is an important mechanism for informing taxation, this knowledge
is useless (c.f. Dillon, 2010) in the absence of an institutional power to enforce said taxation. Allá
is no point being an immaculate prophet of doom if no one believes a word or is willing to do
anything about it.

A similar relation can be seen in Trial C2 regarding t + g and g + F. Although there may be
sufﬁcient institutional power to enforce taxation, the stochastic nature of the stag hunt means that
taxation quickly becomes unfair when resources cannot be redistributed, and a form of oligarchy
emerges.

Por último, the power of each self-organizing mechanism is ampliﬁed when accompanied by
otro, mutually reinforcing mechanisms. This is particularly prevalent when only a subset of the
full range of self-organizing mechanisms is available, as results varied drastically based on the
pairings of mechanisms in the absence of the third. In the following Experiments D, we further
investigate the importance of mechanism selection, as other negative synergies may emerge, semejante
as the superﬂuous signaling identiﬁed here.

5.5 Experiments D: Negative Synergies
Although the overarching trend in all previous experiments, Trials A–C, afﬁrms that an increasing
number of self-organizing mechanisms is conducive to survival, an important criticism to identify is
that these plots are an aggregation of multiple results and offer no insight into what happens “under
the hood”; they merely show the broader picture. Por esta razón, we use this section to illustrate
instances in which self-organizing mechanisms may function in pernicious ways by drawing speciﬁc
attention to the amount of time an island spends in positions of power and the overall resources it
possesses throughout the simulation.

Trial D1 shows a clear case of the iron law of oligarchy, where a purely democratic system has the
capability to degenerate into an oligarchical system. This is suitably evidenced through the poor
resource distribution in D1, in which all islands other than Island 1 are forced to live equally, pero
the lion’s share of resources is withheld (Figure 10a). The explanation for this phenomenon can be
seen in Figure 10b, as Island 1 is able to occupy all roles in parliament. This means that the island is
immune to any form of sanction and receives all additional salaries from the IIGO.

Island 1 is able to remain in power because of the absence of the trading mechanism, significado
that a well-established social network is unable to be formed. Owing to the absence of trade, a case
of individuality is further created by means of positive feedback, as wealth cannot be redistributed.
This experimentation hence demonstrates that, for a fair system, governance must be activated in
parallel with trade, not only to facilitate strong links between the nodes in the social network but to
redistribute an imbalance of wealth.

We contrast this performance to that of the simulation in Trial D2, where trade is activated to
allow for intelligent social network formation. Figure 10c shows a “fairer” distribution of resources,
in which all islands have a similar, if not equal, quantity of resources at each turn of the simulation.
We also identify a less unequal spread of resources when contrasting Figure 10a and 10c, y un
wider spread of institutionalized powers (comparing Figure 10b and 10d), showing that trade is
heavily inﬂuential in equalizing resources across a social network. Además, the distribution of
positions of power in the IIGO is far more randomized, again demonstrating the power of opinion
formation through trade in producing a “fair” system.

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Cifra 10. Distribution of resources and time spent in positions of institutionalized power (roles) in exemplar trials.

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Cifra 11. Visualization of interdependencies between organizations and games. CPR = common-pool resource;
CRD = collective risk dilemma.

En tono rimbombante, both Trials D1 and D2 are successful survival trials, with the average distribution
of resources fairly similar in both cases, barring the dominance of Island 1 in Trial D1. This shows
eso, while the concept of an oligarchy stands in direct opposition to a “fair democracy,” it is not
necessarily disadvantageous for the collective. Por esta razón, we term the emergence of a single
powerful island as an “enlightened dictatorship.”

We also see pernicious interactions between the self-organizing mechanisms by referring back to
Trial A1, where the lack of islands in the archipelago results in overtaxation, ultimately limiting the
prospect of survival. This demonstrates that the choice of activation of self-organizing mechanisms
must be carefully made, relative to both their pairings and the number of islands. This is further
supported by inspection of Figure 11, in which the interactions between games and self-organizing
mechanisms is visualized. Removing any one of these nodes massively affects the cyclical nature of
the interdependencies, which can lead to unexpected effects.

En general, we consider this set of experiments to be a culmination of the previous three sets, como
it unites the key principles from each. Increased uncertainty necessitates increased opportunities
for self-organization, provided this set of self-organization mechanisms is carefully constructed and
underpinned by a critical mass of agents. De lo contrario, it is entirely possible that these mechanisms will
have no positive inﬂuence, potentially leading to instances of oligarchy and superﬂuous signaling.

5.6 Summary of Experiments: Entanglement
The overall conclusion that we draw from these experimental investigations is that there are complex
dependencies between the subgames—and the self-organizing mechanisms are intended to provide
political metagames to help solve corresponding subgames—but that there are also complex de-
pendencies between the political games. It would seem that there is a high level of interdependence
between the subgames and self-organizing mechanisms but also intradependence between the sub-
games and intradependence between the self-organizing mechanisms, as illustrated in Figure 11.

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This entanglement of subgames and self-organizing mechanisms between themselves and each
other reinforces the importance of reﬂection (Landauer & Bellman, 2016), self-awareness (Luis
et al., 2016), and introspection (Holland et al., 2013); their role in reﬂective governance both in
socioecological systems (Dryzek & Pickering, 2016) and in socio-techno-ecological systems (Pitt
et al., 2020); and the importance of cybernetic concepts of stability and viability in self-organizing
sistemas (Ashby, 1952; Beer, 1972). A key point of systemic reﬂection is for components of the
system themselves to balance the tensions between systemic drivers pushing the system to optimize
for polar-opposite values. A similar requirement is observable here: to maintain the tension between
three points (at the level of subgames and the level of self-organizing mechanisms) and between
points at different levels.

6 Related and Further Work

6.1 Trabajo relacionado
We envision this article as helping to unify various other pieces of work concerning variations in
CPR management: LPG games. En esta sección, we explore thematic connections to this research
concerning timing uncertainty and its effect on collective risk (Domingos et al., 2020), institutional
rules for reward and sanctioning (Powers, 2018), and the use of a common pool for disaster pre-
vention (Milinski et al., 2008).

The general theme with these works is that they investigate in greater detail some of the compo-
nents that make up this simulation software. We see this work as a uniﬁcation of simpliﬁed versions
of the related literature, made with the intention of offering insight into an interdependent system.
Por esta razón, while elements of the related work stand present in this article, they serve instead
to build up a more complex, interrelated system.

Looking ﬁrst at Domingos and colleagues’ (2020) work on timing uncertainty, we draw on
the main parallel that a fair criticism of conventional LPGs and CRDs is the limited relevance
to real-world scenarios given the a priori knowledge of the period of disaster and needed threshold.
Domingos and colleagues hence offer a simulation where timing is uncertain and observes the re-
sults of an otherwise conventional LPG. The way in which this article differs is twofold; así como
introducing a second component of uncertainty (through an unknown threshold), we take a differ-
ent approach to what role the purpose of timing uncertainty plays. Domingos and colleagues’ work
investigates how decision-making is affected by timing uncertainty, by creating various strategies for
common-pool contribution. We instead utilize timing uncertainty purely as a means of increasing the
overall uncertainty of the system to evaluate the performance of the different self-organizing mech-
anisms, giving one ﬁxed contribution method based on the time remaining and number of agents
alive. Por esta razón, we conclude that strategic contribution is needed through self-organization,
as randomized taxation is an insufﬁciently powerful technique.

This article also mirrors Powers’s (2018) trabajar, which is predicated on Ostrom institution theory
and how institutional rules can promote cooperation in economic activities. Powers’s paper refer-
ences the fact that both the sharing of information (of other agents) and coordinated systems of
reward and punishment facilitate cooperation in a social network and can help inﬂuence how eco-
nomic interactions occur. From this, Powers provides a model of sanctioning institutions to help
deﬁne explicitly the evolution of institutional rules, looking at the convention of rewarding cooper-
ators and sanctioning (punishing) defectors. We take Ostrom’s and Powers’s insights into this topic
to utilize a system of rules and sanctioning, sin embargo, with great simpliﬁcation. Rule selection in the
case of this article is trivial, putting all predeﬁned rules in play. Although the simulator allows for
rule selection, we again propose a simplistic strategy of random selection with guaranteed approval.
This reﬂects a trivial institutional rule implementation process with little to no evolution. Para esto
reason, we assert that the rule set in this simulator serves only to constitute the governance orga-
nization, effectively creating a simulator with switchable rule activation. Hence we conclude that
sanctioning, taxation strategy, and rules are required for a feasible level of survivability and tie these
attributes together under the umbrella term of governance.

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Finalmente, through investigating Milinski and colleagues’ (2018) trabajar, we see a different approach
to solving a CRD of CPR management. This work looks at the strategy of convincing agents that a
failure to invest enough into the common pool is very likely to cause grave ﬁnancial loss to the in-
dividual. Parallels between this work and Milinski and colleagues’ are visible, particularly in the way
that the resource deduction from each agent’s private pool is controlled. Assuming that the thresh-
old is not met, we use an output scalar to greater deplete the agents’ resources, resulting in a similar
afﬁrmation that a failure to mitigate disaster results in a more severe personal loss. De nuevo, estos
works bifurcate because of the nature of the problem we are looking to solve—we propose that
the collective risk dilemma in contention with two other metagames can be solved through a series of
interdependent self-organizing mechanisms, not just a ﬁxed strategy.

6.2 Further Work
Although we have supplied three feasible self-organizing mechanisms for approaching the prob-
lem of intertwined subgames, it becomes an open question as to whether other socially constructed
mechanisms could also work effectively. This creates an opportunity for further investigation. adi-
cionalmente, experiments could be conducted over more iterations for reproducibility or with a “system
of systems,” where we envision a “super-archipelago” comprising many other archipelagos.

The complexity of this simulation software gives rise to multiple possibilities for future work.
The ﬁrst point to investigate is the prospect of randomizing the disaster frequency, instead giving a
ﬁxed disaster period. This will greatly reduce the power of the current forecasting algorithm (como el
ﬁrst guess that is made is the correct guess, because it is equal to the ﬁrst turn that disaster strikes),
leading to increased randomness in the simulator. Además, the algorithm for this case could be
implemented similarly to the threshold estimation, where a running prediction can be increased and
decreased according to the turn on which disaster strikes.

As well as this, the forecasting organization could be improved to aim to replicate a form of
“foreign aid”: by regressing to the average location of disaster, forecasting could be used to help
predict which agent is likely to be the worst affected during the next disaster. This knowledge could
subsequently be used during trading to give a burst of support to the agent in danger for further
mitigation.

A means of improving the reliability of the forecasting organization (to avoid the fate of
Cassandra alluded to in Experiments D) is through forming a social network inﬂuenced by the
quality of forecasting. Through repeated successful predictions, it can be inductively reasoned that
this will give rise to “experts” with high social standing that are acclaimed for reliable forecasting.
A weighting can subsequently be applied proportionally to the level of expertise to aggregate a ﬁnal,
accurate prediction.

Surplus to this, the current formulation of the simulator naturally gives rise to a machine learning
approach in many aspects. Regression algorithms can be applied to the role of President to determine
the optimal level of taxation, or a classiﬁcation algorithm can be used to deﬁne the various rules
as beneﬁcial or not. Naturalmente, any aspect of the simulator that introduces the possibility of choice
may be solvable through modern machine learning methods; sin embargo, it may limit the system’s
heterogeneity.

7 Summary and Conclusions

En resumen, the contributions of this article are threefold:

1. We have deﬁned an innovative analytical and experimental scenario for exploring

cooperative survival games with four parameters: escala, incertidumbre, complejidad, y
opportunity for self-organization.

2. We have designed, especificado, and implemented a self-organizing multiagent system with

new algorithms for three self-organizing mechanisms: trading, pronóstico, and governance.

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3. We have conducted a series of experiments that have shown the following:

– Complex cooperative survival games are solvable given a critical mass of

survivors and some opportunity for self-organization.

– Even with critical mass, increasing dimensions of uncertainty and complexity

require more and “better” opportunities for self-organization.

– Sin embargo, self-organizing mechanisms can interact in mutually supporting ways

but also in unexpected ways with potentially pernicious outcomes.

In more detail, the general trend observed in all the survival trials is that, irrespective of uncer-
tainty, the survival chance increased as more self-organizing mechanisms were made available. El
main exception was in the case of total certainty, in which the presence of forecasting offered no
greater chance of survival than without: It would seem, like Cassandra, that there is no point being
an immaculate prophet of doom if no one believes a word or is willing to do anything about it, en el
absence of either some form of coercive authority (Olson, 1965) or some decentralized incentive to
collective action (Ostrom, 1990).

This observation indicates that while the three subgames of the cooperative survival game are
interdependent, the self-organizing mechanism designed to help solve each subgame does not work
in isolation either, and these mechanisms can be mutually supporting. The experiments showed that
introduction of more self-organizing mechanisms can provide increasing beneﬁt, as the interplay
between such mechanisms allows for a greater range of possible actions and hence multiple ways
of assessing the different metrics in the social system. A particular example of this is how the
friendship value shared between agents may be initially formulated through trade; sin embargo, this was
reevaluated through their willingness to broadcast taxation in government.

Además, increased uncertainty yielded an overall lower survival chance, irrespective of the
number of active mechanisms; sin embargo, there were most instances when a 100% survival chance
was maintained when all three mechanisms were active. This showed that the self-organizing mech-
anisms are sufﬁcient for allowing cooperative survival throughout all levels of disaster uncertainty;
relativamente, aunque, the performance of all three mechanisms, when active, relative to one acting
solo, is much greater than the sum of its parts.

Sin embargo, while an increase in uncertainty necessitates an increase in opportunities for
self-organization for a successful solution, the experiments also demonstrated that interplay can
be potentially pernicious and furthermore required the active participation of sufﬁcient agents for
the self-organizing mechanisms to ensure a positive rather than a pernicious inﬂuence (es decir., incluso
the subgames required a critical mass of “players,” as well as the overall cooperative survival game
requiring a critical mass of survivors).

En conclusión, entonces, the introduction of multiple self-organizing mechanisms to complex and
sensitive situations should be carefully designed to ensure that such mechanisms are mutually
supportive—with the strong caveat that the intended beneﬁcial and prosocial relationship is not
always instantly obvious and should not be taken for granted. Sin embargo, we would contend that
this is precisely the kind of complementary insight that ALife simulations of the kind described
here can bring to applications like statistical epidemiology for public health policy making, popula-
tion modeling for urban planning, and legal modeling for informing legislative drafting. We need to
know what happens when people are empowered with tools to reshape their own environment, y
what happens (such being the power of generativity) when they reshape the tools in ways that the
designers never intended or even imagined.

Because it is always possible to game the metagame, effective processes for reﬂection in col-
lective self-governance will be critically important in the future. Reﬂection is, loosely speaking, el
idea that in control systems, some components have an internal model of the system (incluido
ellos mismos), can reason about its (the system’s and the component’s) behavior and performance,
and can adjust or reconﬁgure some of the control variables or parameters accordingly (Ashby, 1952;

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Landauer & Bellman, 2003). The need for such reﬂection has been identiﬁed for self-governance,
has been studied computationally in diverse contexts such as self-improving systems for systems
integración (Bellman et al., 2014), and has motivated the need for run-time models (Landauer
& Bellman, 2016). The idea of reﬂection has also featured in recommendations for the collec-
tive self-governance of socioecological systems (Dryzek & Pickering, 2016) and algorithmic self-
governance of socio-techno-ecological systems (Pitt et al., 2020). Especially in those latter contexts,
where sustainability is such a key feature, the current study highlights the need for reﬂection not
just as a matter of ALife but as a matter of ALife and ADeath as well.

Expresiones de gratitud
We are especially grateful to the anonymous reviewers for their many helpful and insightful com-
mentos. This work is partly based on the simulator developed during the COVID-19 pandemic by the
Imperial College Department of Electrical and Electronic Engineering SOMAS cohort, 2020–2021.

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