The Effects of Information on the - Ricerca sull'intelligenza artificiale specializzata al MIT

The Effects of Information on the
Formation of Migration Routes
and the Dynamics of Migration

Abstract Most models of migration simply assume that migrants
somehow make their way from their point of origin to their chosen
destination. We know, Tuttavia, that—especially in the case of
asylum migration—the migrant journey often is a hazardous,
difﬁcult process where migrants make decisions based on limited
information and under severe material constraints. Here we
investigate the dynamics of the migration journey itself using a
spatially explicit, agent-based model. In particular we are interested
in the effects of limited information and information exchange.
We ﬁnd that under limited information, migration routes generally
become suboptimal, their stochasticity increases, and migrants arrive
much less frequently at their preferred destination. Under speciﬁc
circumstances, self-organised consensus routes emerge that are
largely unpredictable. Limited information also strongly reduces the
migrants’ ability to react to changes in circumstances. We conclude,
ﬁrst, that information and information exchange is likely to have
considerable effects on all aspects of migration and should thus be
included in future modelling efforts and, second, that there are many
questions in theoretical migration research that are likely to proﬁt
from the use of agent-based modelling techniques.

Martin Hinsch*
University of Southampton
Department of Social Statistics

and Demography

University of Glasgow
MRC/CSO Social and

Public Health Sciences Unit

hinsch.martin@gmail.com

Jakub Bijak
University of Southampton
Department of Social Statistics

and Demography

Keywords
Migration, communication, beliefs,
migration routes, agent-based modelling

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1 introduzione

International migration has important economic, humanitarian, and cultural consequences not only
in countries of origin and destination but also in countries that lie on common migration routes
(Castles et al., 2014). Nevertheless migration is to date one of the least well understood demographic
processes (Bijak et al., 2021). The majority of older theoretical efforts to understand migration follow
the economic tradition where migrants’ behaviour is typically described as an optimisation process
that weighs the costs of migration against a combination of push and pull factors in the countries
of origin and destination, rispettivamente (Greenwood, 2005). While some of these models have be-
come quite sophisticated and have in some cases even been empirically validated, the approach has
repeatedly been criticised for oversimplifying many aspects of the system (Klabunde & Willekens,
2016).

In particular, it is usually assumed that migrants’ decisions follow a simple and rational process.
Furthermore variation between individuals as well as interactions between them are usually not taken

* Corresponding author.

Artiﬁcial Life 29: 3–20 (2022) https://doi.org/10.1162/artl_a_00388

M. Hinsch and J. Bijak

Formation of Migration Routes

into account. Why these assumptions might limit the applicability of these models is demonstrated
by empirical results that show that in many cases prospective as well as actual migrants are substan-
tially misinformed concerning the conditions in the country of destination (Gilbert & Koser, 2006).
It has also been found that connections to and opinions of a country within an individuals’ social
network can play an important role in the migration decision, thus making interactions between
individuals relevant for the process (Saˇcer et al., 2017).

Some of these concerns have been adressed in newer modelling efforts, in particular those
using agent-based modelling (Frydenlund & De Kock, 2020). By explicitly simulating single in-
dividuals, agent-based models make it straightforward to model variation and interactions within
a population. Inoltre, since these models are usually computational there is no inher-
ent limit to the complexity of behaviour that can be modelled (for an overview see Hinsch & Bijak,
2021).

An aspect of migration that has not received much attention amongst modellers, even in newer
studies, is the migration journey itself. The main reason for this is probably that in most models
of migration the focus lies on the decision to migrate and then on the choice of destination. Some
predictive models tailored to a speciﬁc time and place explicitly include the migrants’ travels (per esempio.,
Frydenlund et al., 2018; Hébert et al., 2018; Suleimenova & Groen, 2020) but apart from our own
earlier work (Hinsch & Bijak, 2019), we are not aware of any theoretical models that directly inves-
tigate or take into account individuals’ movement. Migrants are instead assumed to make their way
from origin to destination without further complication.

We know, Tuttavia, that migrants’ journeys are anything but simple, direct movements from
a country of origin to a destination (Crawley et al., 2016; Kingsley, 2016). More importantly, IL
speciﬁcities of the journey might have consequences in other areas as well. They can be relevant in a
practical context, COME, Per esempio, political as well as humanitarian reactions to migration depend on
the timely localizing of migrants. In a theoretical context on the other hand they might affect our un-
derstanding of migration itself, as decisions made during travelling might have profound carryover
effects on other aspects of migration such as choice of destination (Brekke & Brochmann, 2015).
Furthermore the difﬁculty of the journey a migrant expects will change the perceived attractiveness
of destinations and might therefore itself affect their choice of destination or even the decision to
migrate in the ﬁrst place (Bertoli & Fernández-Huertas Moraga, 2013).

While the effect of limited information about migrants has been considered at least in the eco-
nomic literature (Katz & Stark, 1987), migrants themselves are usually assumed to be perfectly
informed. Information can, Tuttavia, be an important yet often scarce resource for migrants during
their journey. Surveys of migrants show that knowledge about the destination and the ways to reach
it is often limited and might come from unreliable sources (Borkert et al., 2018; Dekker et al., 2018;
Gilbert & Koser, 2006). In some cases this information precarity is exacerbated by a general dis-
trust towards information sources other than personal contacts (Emmer et al., 2016). If, Tuttavia,
migrants base their travel decisions on incomplete or erroneous information, it can be expected that
they will experience difﬁculties on their journeys leading to delays, detours, or failure.

As we showed in an earlier theoretical simulation study, this scarcity of information and the
way knowledge is obtained and exchanged can indeed strongly affect the development of migration
routes. We found that under limited information, migration routes can become an emergent effect
of the migrants’ communication, which makes them unpredictable and leads to suboptimal travel
(Hinsch & Bijak, 2019). This suggests that the assumption of a straightforward, successful migration
journey might often be misleading.

Here we expand on this effort using an improved version of the model. Our aims in this are
twofold. First we want to test the robustness of our previous results in a more general context
and with a better model. Mainly, Tuttavia, we are interested in how misleading we expect the
assumption—as made in most migration models—of a simple journey with perfect information
to be. Our question therefore is: How different are migration journeys under perfect information
from those in a scenario with limited information? What might the consequences of these differ-
ences look like?

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Formation of Migration Routes

It is important to note that as with our previous study this is a purely theoretical work. We are
not modelling a speciﬁc real-world situation but performing computational sociology (Macy & Willer,
2002) by attempting to understand the effect of certain assumptions on the behaviour of an entire
class of systems.

2 Model Description

The model described below is a strongly modiﬁed version of a model we have presented before
(Hinsch & Bijak, 2019). Along with many smaller modiﬁcations, we transitioned from stepwise up-
dates to a continuous-time, event-based paradigm (with commensurate changes from probabilities
to rates and updates to processes) and simpliﬁed the model by removing capital, resources, and the
two-tier link system.

An earlier version of the model that the present study is based on was also used as a didactic

running example in our book (Bijak et al., 2021).

Since a full description of the model would exceed the available space, we provide in the follow-
ing only a brief overview. The source code and detailed documentation for the model can be ac-
cessed on Comses (https://www.comses.net/codebases/b57ed5e2-47cb-4b61-9d95-8785398c6c8d
/releases/1.1.0/). Please note that a few of the mechanisms described in the full documentation
(risk, resources, and capital) were not used in the current study and were therefore switched off
in the simulation runs by setting the appropriate parameter values. A full list of model parameters
including default values can be found in the appendices.

2.1 Overview
In our model a population of migrants travels from a location of origin to a destination, crossing
a landscape of cities and transport links. Agents attempt to navigate this world optimally based on
subjective knowledge that is not necessarily complete or correct. They gain additional knowledge
through experience and by exchanging information with other agents.

2.2 Entities
The simulated world consists of locations (“cities”) that are connected by links (Guarda la figura 1). Cities
and links are static entities with properties that do not change over the course of the simulation.
Cities have a 2-dimensional position and a quality that determines their attractiveness to agents. Quality
represents, Per esempio, IL (lack of) presence of police, the availability of resources, or the level of
sicurezza. Links connect two cities and have friction as their only property. Friction affects the time it
takes for an agent to transverse the link and is determined by the link’s length as well as a stochastic
component.

Nearly the entire behaviour of the model consists of the actions of agents or their interactions
with each other or the world (see below). Agents are at all times positioned either in a city or on
a link unless they have arrived at their destination. Agents have some amount of information about
the world (see below) as well as a number of contacts among the population of travelling or arrived
agents.

2.3 World
The simulated world is constructed as a random geometric graph (Gilbert, 1961) Di 600 cities con-
nected by transport links. Cities have a random quality q ∼ U[0,1]. The positions of cities are dis-
tributed uniformly on a unit square. Any two cities that are closer than a threshold distance are
connected by a transport link. In addition one departure location at x = 0, y = 0.5 E 10 exit

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Formation of Migration Routes

Figura 1. Diagram of the entities in the model and their relationships.

locations placed in regular intervals at x = 1 are added to the world. Departure and destination
locations are connected by links to the ﬁve closest cities, rispettivamente.

Links’ only property is friction, which is calculated from distance d as fi = dir with random

r ∼ U[0.75,1.25].

2.4 Actions and Interactions
All events in the model are assumed to be Poisson processes in continuous time. With the exception
of the creation and departure of new agents, all changes of model state are the result of the action of
an agent. Which actions an agent can perform and their rates of occurrence depend on the agent’s
state, in particular on whether it is currently travelling on a link or staying in a city.

create agents Agents are created with a ﬁxed time-dependent rate. They enter the world at the
departure location. Unless noted otherwise, agents start out without contacts and without
any knowledge.

plan During planning, an agent either plans a route to an exit or, if it does not have sufﬁcient

knowledge, decides which neighbouring city to go next.

explore An exploring agent gains new knowledge about closeby cities and links.

add contact An agent adds agents that are currently situated in the same city to its list of contacts.

forget contact An agent unilaterally forgets a randomly selected contact.

exchange information An agent communicates with one of its contacts and exchanges informa-
tion about the world topology, cioè., the existence and connectedness of cities and links, anche
as their properties.

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Formation of Migration Routes

depart An agent departs from its current location and starts travelling to the next location in its

plan.

arrive A travelling agent ﬁnishes traversing a link.

2.5 Information
We are interested in how reliance on and exchange of possibly incomplete or wrong information
affect the agents’ decision-making. Therefore we decided to explicitly model the agents’ knowledge
of the world as well as the information exchange between agents. The submodel on information
exchange presented in this section is largely identical to earlier versions published elsewhere (Bijak
et al., 2021; Hinsch & Bijak, 2019).

An agent’s knowledge is comprised of a number of information items each of which represents a
city or a link. Topologically this information is accurate—all connections an agent knows about are
correct—but not necessarily complete—an agent may know only a small number of cities and links.
Information items have the same properties as the real-world entities they represent; Tuttavia, their
values may be inaccurate.

To model this, the real values of properties are in their subjective counterpart replaced by an
estimate of the value together with a certainty that the value is correct. Agents can gain information
either directly from the world by “exploration” (action ‘explore’) or by communicating with other
agents (action ‘exchange information’). As explained in the following, both processes can add new
information items and update an estimate as well as the certainty of an information item’s properties.
If agents encounter unknown (to them) cities or links (through exploration or communication),
they add a new information item corresponding to that entity to their knowledge, setting property
estimates to a default value and certainty to 0. When exploring a known entity, values are updated,
with the new value being a weighted mean between the previous estimate or certainty and the real
value (O 1 in case of certainty).

Information exchange between agents is more complicated as it needs to exhibit a number of
speciﬁc properties: If two interacting agents have similar estimates for a property their correspond-
ing certainty should increase. If, on the other hand, their estimates differ, both individuals should
decrease their certainty. Allo stesso tempo, an agent should always adjust its estimate in the direction
of that of its interaction partner; Tuttavia, it should do so in proportion to its relative certainty. Quello
È, in an exchange between an agent with high certainty and one with low certainty, the agent with
the low certainty should change its estimate more.

While there is a substantial theoretical literature on belief and opinion dynamics, previous models
seem to focus largely either on adversarial exchange of opinions, cioè., situations where individuals
attempt to convince each other, or on situations where individuals change their beliefs according
to social norms or consensus (per esempio., Duggins, 2017). An interesting approach by Martins (2009) E
extended by (among others) Adams et al. (2021) uses Bayesian inference to derive updating rules
for beliefs about the value of continuous real-world variables. The resulting model is, Tuttavia,
computationally quite expensive. We therefore designed our own model of information exchange.
We based our information model on the well-known mass action dynamics (Horn & Jackson,
1972). To understand the model it is best to imagine that an agent’s belief consists of two “sub-
stances”, certainty and doubt, in proportion t and d = 1 − t. When two agents interact a “reaction”
between their respective belief components takes place, potentially transforming them: Doubt re-
acting with doubt produces doubt. Certainty of one agent interacting with the other agent’s doubt
can “convince” the latter, changing parts of its doubt into certainty. Depending on the difference
in estimate, certainty interacting with certainty can lead to confusion and increased doubt or just
change the estimate.

More formally, for an interaction between agents A and B with an estimate v we deﬁne the

difference in estimate as

δv :=

|vA − vB|
vA + vB

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(1)

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Formation of Migration Routes

Using parameters ci (“convince”), cu (“confuse”), and ce (“convert”), we then calculate the new doubt
value d ′

A based on the previous values of certainty t· and doubt d· as

d ′
A = dAdB + (1 − ci)dAtB + cutAtBδv.

The estimate vA changes accordingly:

v′
A =

tAdBvA + cidAtBvB + tAtB(1 − cuδv)((1 − ce)vA + cevB)
1 − d ′
UN

(2)

(3)

It is important to note that this is a purely phenomenological model. It was chosen for being
based on a well-known, simple formalism and showing all required properties, but does not claim
to be psychologically or empirically accurate. As we can see, for the special case where different
opinions do not lead to doubt, cioè., cu = 0, doubt will disappear, cioè., d will approach 0 (as long as
ci > 0), and the model reverts to a simple weighted mean (as in, Per esempio, Nordio et al., 2018):

v′
A = (1 − ce)vA + cevB

(4)

2.6 Decisions
Agents attempt to ﬁnd the least costly route from their current position to an exit, based on their
current knowledge. The cost of a route is a function of the links’ friction and the quality of cities
visited on the way. If they are not able to ﬁnd a complete path they instead select the best city in the
vicinity based on distance (friction), quality, and proximity to the destination.

2.7 Setup
We are investigating the effects of (limited) information and information exchange on the formation
of migration routes. In order to obtain a baseline with which to compare our results, we ﬁrst ran
all scenarios under the assumption of perfect information. Questo è, agents received full and perfect
knowledge about every link and city in the simulated world. In order to avoid any additional ef-
fects through communication errors we also switched off communication in these scenarios entirely
(see Appendix 1).

To test the effects of information exchange we then ran the model under various levels of com-
munication frequency and intensity (see Table A1 in Appendix 1). We also varied the strength of
communication error and the ﬁdelity of the information agents receive through exploration.

We explored further potential real-world consequences of information in additional scenarios
where agents had a preference for a speciﬁc destination (scenario ‘preferred destinations’) or where
after a certain amount of time some links became difﬁcult to navigate (scenario ‘intervention’).

We ran 10 random replicates for each parameter combination. As preliminary runs showed
that the simulation approaches equilibrium after 300–500 time units, we ran all simulations up
to t = 750.

3 Results

We wanted to know whether discrete migration routes form in the ﬁrst place and, if so, how pre-
dictable and optimal they are. For this we used three key measurements:

route concentration We calculate the relative standard deviation of transit counts across all links

as a proxy for the degree to which travel routes are similar between agents.

optimality We determine the correlation coefﬁcient between realised transit counts for all links
and transit counts in a hypothetical scenario where each individual travelled optimally.

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unpredictability The unpredictability of transits for a given city is measured as the standard de-
viation across all replicates of the proportion of transits for that city. We calculate overall
unpredictability as average unpredictability of arrivals over all exits.

3.1 Baseline Scenario
If individuals are perfectly informed, every agent is able to ﬁnd and travel on the optimal route,
resulting in maximum route concentration and predictability (Figura 2). With imperfect or incom-
plete information agents do not necessarily know enough to ﬁnd the objectively best route and will
instead travel suboptimally (Figura 3). This leaves scope for variation between individuals as well as
between replication runs (Guarda la figura 4), therefore route concentration as well as route predictability
are substantially lower in scenarios without perfect knowledge (Figura 2).

As we can see in Figure 2, Tuttavia, for anything but perfect exploration, the unpredictability of
agent arrivals decreases when changing from low to medium communication but increases again for
high communication. Together with the increase in route concentration with communication, Questo
indicates that what we observe is a phase transition between three regimes:

For low communication, agents receive only little input from each other. D'altra parte
exploration is not sufﬁcient to produce a reliable map. Routes therefore differ between agents and

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Figura 2. Route concentration (top, see text for deﬁnition) and unpredictability (bottom, see text for deﬁnition) for
different values of exploration, communication, and communication error. The black line indicates values in a scenario
where individuals have perfect information and do not communicate. We see that while higher levels of communication
lead to an increase in route concentration, arrivals are most predictable at intermediate levels of communication.

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Formation of Migration Routes

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Figura 3. Average travel time (top) and route optimality (bottom, for deﬁnition see text) for different values of ex-
ploration, communication, and communication error. The black line indicates values as obtained in a scenario where
individuals have perfect information and do not communicate. Travel time is high and increases with error for low
communication while it is low and decreases with error for medium and high communication. Routes are generally
closer to the optimum for intermediate levels of communication.

from the optimal route, leading to strong stochasticity across replicates (and thus high unpredict-
ability).

For medium communication information, transfer between agents is high enough that a relatively
accurate and complete consensus map emerges in the population. This leads to the emergence of
similar, predictable, and relatively optimal routes in most replicate runs.

For high communication, the consensus between agents is even stronger. Tuttavia, now the
effects of information transfer override the effects of exploration so that unreliable consensus maps
emerge. Therefore, while most agents take a similar route, that route is less optimal than for medium
communication and can vary from case to case (implying lower predictability).

3.2 Preferred Destinations
With our second set of scenarios, we investigated how information and communication affect the
chances of migrants to reach their preferred destination. For this we assumed that each agent
at random picks one of the 10 destinations as its preferred target. The strength of preference

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Formation of Migration Routes

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Figura 4. Migration trajectories for different scenarios. Thickness of the lines indicates trafﬁc; colour represents friction
(red: high). The top left panel shows the result for a full knowledge scenario (and thus the optimal path). The other
panels are taken from communication scenarios. Top right: no error, low exploration, low communication; bottom left
and right: low error, high exploration, high communication, different random seeds.

then indicates the increase in travel costs an agent is willing to incur in order to arrive at that
destination.

Except for decreased route concentration (due to agents attempting to reach their target exits),
adding preferences has little effect on the behaviour of the model as presented above (not shown).
With respect to the ability of agents to follow their preferences, we ﬁnd that if agents have perfect
information a preference of 30% is sufﬁcient to let the vast majority reach their preferred destina-
zione (Figura 5). Without prior information, Tuttavia, in most scenarios less than half of the agents
manage to arrive at their target. As before, agents travel most optimally for medium communication
and high exploration, but even under these conditions arrival at target remains below 70%.

3.3 Interventions
A common response to a sudden increase in migration is the erection of physical or administrative
barriers in the form of, Per esempio, border closures or transport restrictions (Andersson, 2014).
In our third set of scenarios we investigate how the reaction of migration routes to the sudden

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Figura 5. Proportion of agents arriving at their preferred destination for different values of exploration, communication,
communication error, and strength of preference. The black line indicates values as obtained in a scenario where
individuals have perfect information and do not communicate. Only for high error rates during communication and if
agents are willing to incur an additional cost of 30% (bottom graph) do substantial proportions arrive at their preferred
destination.

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Figura 6. Properties of migration routes for an intervention scenario (see text for deﬁnitions). The black line indi-
cates values from an equivalent scenario with full knowledge. After the intervention the quality of routes decreases
dramatically while travel times increase substantially (cf. Figures 2 E 3).

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Formation of Migration Routes

Figura 7. Migration trajectories for scenarios with interventions. Thickness of the lines indicates trafﬁc; colour rep-
resents friction (red: high). The vertical dashed line represents the barrier. Shown are the results for full knowledge
(left) and limited knowledge (right) with high error, perfect exploration, and low communication; both with a prefer-
ence value of 30%. While agents easily manage to circumvent the obstacle when they are fully informed, only a small
proportion of agents does so in the limited-information scenario.

appearance of barriers depends on the information regime. We implement barriers by, at timestep
500, increasing friction in all links that intersect with a vertical line across 80% (Guarda la figura 7) Di
the world to 0.9 (which corresponds to an increase in travel time of about 8 time units). As we
can see in Figures 6 E 7 migration routes in scenarios with full knowledge change to accomodate
the barrier, so that neither quality nor travel time are substantially affected, although the number of
agents reaching their preferred destination decreases as an effect of the detour.

In information-limited scenarios on the other hand, migration routes are largely unable to adapt.

The quality of routes plummets and travel times increase substantially.

4 Discussion

We have shown that limitation and exchange of information can have a strong inﬂuence on the
formation of migration routes. Migration routes can become less optimal, less predictable, and less
centralised if migrants do not have perfect knowledge. Furthermore the proportion of migrants
reaching their preferred destination is substantially lower in scenarios with more realistic informa-
tional logistics, and migrants ﬁnd it much more difﬁcult to adapt their routes to changing circum-
stances. The exchange of information in particular has a counterintuitive effect in that under certain
conditions higher levels of communication can lead to less predictable routes (see also Hinsch &
Bijak, 2019).

Even though this is a relatively simple, theoretical model, we can already at this stage draw
a number of conclusions concerning migration modelling as well as the real-world dynamics of
migration.

First and foremost we can conclude that information and information exchange are likely to
be relevant for the formation of migration routes in the real world. In our model, how much in-
formation the agents have available and the frequency and accuracy of information exchange can
lead to qualitatively different properties of the migration routes observed in the system. We know
that in reality migrants do in fact often make travel decisions based on limited knowledge (Borkert
et al., 2018; Crawley et al., 2016). It has also been found that (depending on country of origin) Di-
ﬁcial sources of information are often met with very little trust and that in these situations most
information is gathered from peers (Emmer et al., 2016; Prike et al., 2022). It seems therefore
reasonable to expect that effects similar to those observed in our model can be found in reality.

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Consequently any modelling attempting to predict migrants’ movement in detail or on a small scale
will need to incorporate these effects. This is particularly salient where models are meant to be
used to support humanitarian measures in crisis situations. Previous modelling efforts in this area
assume perfect knowledge (albeit sometimes with a limited range of perception) and thus optimal
decision-making (per esempio., Frydenlund et al., 2018; Hébert et al., 2018; Łatek et al., 2013; Suleimenova
& Groen, 2020). We expect that including the effects of information in these models would change
at least some of the observed results.

We also see that the migration journey itself not only shows considerable variations in dynamics
depending on which scenario we assume but also can have important effects on other aspects of
migration. Our results show that introducing a (more) realistic information regime can halve the
number of migrants that arrive at their preferred destination. This contradicts the assumption of
many models of migration that migrants always arrive at their chosen destination (per esempio., Ahmed et al.,
2016; Lin et al., 2016). We can conclude that while the situation might be different for voluntary
migration, at least models of forced migration should assume that a considerable proportion of
migrants will be diverted on their journey and that this depends on the information regime in the
population. Similarly the effects of introducing a barrier to migration differ considerably depending
on whether we assume perfect information or not. Models that, Per esempio, attempt to extrapolate
the effect of border closures on migration will risk vastly overestimating the effectiveness in steering
migration streams unless the role of information is included.

The situation becomes even more complicated when we look in more detail at how the speciﬁc
variables we modelled correspond to aspects of real-world situations. The frequency and accuracy
with which migrants communicate might be a result of cultural factors but will also depend on
simple practical aspects of their circumstances, such as availability of mobile phones, opportunities
to charge them, and accessibility of service in the travel area (Gillespie et al., 2018). Similarly the
access to local information (exploration in our model) can be strongly affected by something as
straightforward as a language barrier. Empirical studies furthermore show that how well informed
migrants are about their journey and their destination as well as their capacity to obtain information
can vary dependent on factors such as country of origin (Dimitriadi, 2018; Emmer et al., 2016).
Based on our results it can therefore be expected that migrant populations will differ, Per esempio,
with respect to how predictable their travel routes turn out to be or how likely it is that migrants end
up at their planned or preferred destination. Modelling studies aiming at predicting migrant arrivals
therefore have to take the speciﬁc properties of the modelled population as well as how they relate
to the situation into account.

Even though the importance of networks for migration decisions has been recognised in previ-
ous studies (Gurak & Caces, 1992), many models that explicitly include networks simplify them in at
least one of two ways—by assuming that networks do not change over time (per esempio., Simone, 2019), O,
if so, then deterministically and/or or by summarising the effects of networks as a single numerical
value (per esempio., “strength” or “number of connections”; per esempio., Lin et al., 2016) that then is used during
decision-making. Our results show that the situation can be considerably more complicated. Noi
ﬁnd that not only the existence and strength of the network matters, but also what individuals use
it for. In our case that is information, but it does not seem implausible that other, known, rete
effects such as monetary support or logistic aid have similarly ﬁne-grained dynamics that affect the
other parts of the system and therefore need to be taken into account.

4.1 Limitations and Future Work
While our results clearly show that informational logistics affect the migration journey, it is difﬁcult
to judge how exactly the scenarios we investigated relate to speciﬁc real-world situations. A questo
point our modelling efforts therefore have to remain a proof of principle. Tuttavia, given the wide
range of parameter values we tested, we can assume that similar dynamics will take place in real
systems. Nevertheless, additional effort will be required to calibrate the model to empirical data in
order to test the relevance of our results.

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We intentionally kept our model of information and information exchange simple and ab-
stract, partially due to a lack of reliable empirical information and partially in order to investi-
gate the simplest scenarios ﬁrst. At this point the model is therefore clearly “unrealistic” in many
aspects. The two biggest simplifying assumptions concerning information in our model have to
be, ﬁrst, that agents (in the “communication” scenarios) have no prior knowledge and, second,
that information is retained and exchanged entirely indiscriminately. Strictly speaking both as-
sumptions are clearly wrong. In the absence of empirical data on either aspect, Tuttavia, any
attempt at making the model more realistic would have lead to a massive increase in the num-
ber of potential realisations and in the size of the parameter space. As it is, this version of the
model and the scenarios we tested serve to describe both extremes of what is possible in reality.
Any real population will likely be somewhere between our “full knowledge” and “no knowledge”
scenarios.

In this version of the model we assume for the sake of simplicity that the only choice agents
have is which route to take. We know, Tuttavia, that in reality migrants have more options available.
For one they may decide that they would be better off returning to their country of origin when,
Per esempio, faced with an obstacle. More importantly, Tuttavia, there are many situations where
it can be prudent or even necessary to delay the continuation of the journey (Anam et al., 2008;
DeVoretz & Mamma, 2002). If included this would add timing of migration decisions as an important
dimension to the model.

We also completely ignored the heterogeneity that every human population shows. We know
that means and circumstances often differ between early and late migrants on the same route
(Lindstrom & López Ramírez, 2010). If we assume that access to information differs in a simi-
lar way, we can easily imagine that well- or better-informed early migrants serve as “trailblazers,"
chosing good routes and transmitting their experiences to followers who a priori might not be as
well-informed.

Another aspect worth exploring in the future that was out of scope for this study is the role
of network structure and density in information transmission and—ultimately—route formation.
To a certain degree we can assume that, Per esempio, the effects of an increase in information ex-
change due to higher network density are analogous to the effects of increased information exchange
we modelled in our scenarios. Tuttavia, new dynamics might emerge if networks interact with
other aspects of the system, Per esempio, if people have a tendency to travel in groups (Collins
& Frydenlund, 2016) or if pre-existing networks are stratiﬁed by social status and thus access to
information and capital.

We also—again for the sake of simplicity—did not include many of the additional factors known
to be important in real-world migration systems. There are, Per esempio, good indications that
at least in some situations, smugglers play an important role in maintaining or even shaping mi-
gration routes, in particular when there are pre-existing non–migration-related smuggling routes
(Triandafyllidou, 2018). We also completely ignored the effects of material means on the avail-
ability of information and transportation (see the point on temporal heterogeneity above).

Furthermore the difﬁculty of the journey a migrant expects might itself affect their choice of
destination or even the decision to migrate in the ﬁrst place. Tuttavia, that difﬁculty itself might
decrease over time if a migration route emerges and leads to the establishment of supporting
infrastructure. In this case the migration decision is therefore part of a feedback loop and cannot be
understood without taking into account the journey.

4.2 Conclusions
We can conclude that information is an important, yet largely neglected aspect of migration that
deserves more attention in the future. This is likely to apply to all stages of the migration journey,
from the decision to leave to the journey itself to the decision to remain in the country of arrival
or to move on, and ﬁnally in the decision to return if the opportunity arises. Our model is a simple
ﬁrst step in exploring this issue that—as discussed above—leaves ample scope for extension. Noi
are looking forward to seeing the interesting future developments in this area.

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Our work also conﬁrms that—as is the case for many other social phenomena—small-scale
interactions between individuals can have substantial effects in the context of migration. While
it might for a given situation be possible to ﬁnd macroscopic approximations for the effects of
microscopic interactions this can be a difﬁcult and time-consuming process. If we assume that
information exchange is not the only relevant interaction between migrants (others include direct
interactions such as transfer of capital and indirect interactions via environmental factors, ad esempio
economic effects of transit zones or the establishment of smuggling services)—we have to conclude
that in many if not most situations some form of bottom-up modelling strategy will be required
when dealing with the dynamics and effects of migration (Willekens, 2018). This further strengthens
the case for the use of agent-based modelling in the social sciences (Chattoe-Brown, 2013).

Ringraziamenti
This work has received funding from the European Union’s Horizon 2020 research and innovation
programme; European Research Council grant No. 725232 BAPS: Bayesian Agent-Based Popu-
lation Studies (MH and JB). This article reﬂects the authors’ views, and the Research Executive
Agency of the European Commission is not responsible for any use that may be made of the in-
formation it contains. We are grateful to the anonymous reviewers for their comments that helped
improve an earlier draft of the manuscript.

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Appendices

Appendix 1: Scenario Parameters

Formation of Migration Routes

Table A1 shows the parameters that vary between scenarios. Scenarios ‘preferences’ and ‘obstacle’
were run in combination with all conﬁgurations for ‘full info’ and ‘communication’, rispettivamente.

Table A1. Parameters that vary between scenarios.

Parameter

n_ini_contacts

p_know_target

p_know_link

p_know_city

speed_expl_ini

n_contacts_max

p_drop_contact

Explanation

Full info

Communication

Preferences

Obstacle

Initial number of
contacts

Probability to know an
exit at the start of the
simulation

“Link”

“City”

Exploration on
departure

Maximum number
of contacts

Probability to lose a
contacts

1.0

0.0

1.0

0.0

0.05

var

pref_target

Preference for speciﬁc
destination

1.0

1.1, 1.3

1.0, 1.3

convince

See section 2

convert

confuse

See section 2

error, error_frict

Communication error

rate_explore_stay,
p_ﬁnd_links,
p_ﬁnd_dests,
speed_expl_stay,
speed_expl_move

Rate of exploration and
quality of information
gained when exploring

p_keep_contact,
p_info_contacts,
p_transfer_info

Probability to gain
contacts, rate of
information exchange

0.0

n.a.

0.5

0.1

0.3

{0.0, 0.0},
{0.12, 0.015},
{0.36, 0.045}

{1.0, 0.1, 0.1, 0.5, 0.5},
{4.0, 0.8, 0.5, 1.0, 1.0},
{10.0, 1.0, 1.0, 1.0, 1.0}

var

{0.1, 0.1, 0.1},
{0.3, 0.3, 0.3},
{0.6, 0.6, 0.6}

var

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Formation of Migration Routes

Some parameters were changed as a set (indicated as ‘{}’). Error level for example changes both,
error and error_frict. A value of ‘{0.12, 0.015}’ then corresponds to a value of 0.12 for error and 0.015
for error_frict.

Appendix 2: Default Parameter Values

Table A2 shows the values of all parameters that do not change across the scenarios. The submodels
on risk and resources, rispettivamente, were not used and the corresponding parameters have been
omitted.

Table A2. Values of all parameters that do not change across scenarios.

Parameter

n_cities

link_thresh

n_exits

regular_exits

n_entries

regular_entries

exit_dist

entry_dist

n_nearest_entry

rate_dep

rate_plan

res_exp

qual_exp

frict_exp

qual_weight_x

qual_weight_res

qual_tol_frict

Default

600

0.12

VERO

1.0

0.0

20.0

100.0

0.5

1.25

0.25

0.0

2.0

Parameter

n_nearest_exit

qual_entry

res_entry

qual_exit

res_exit

dist_scale

frict_range

p_unkown_city

p_unknown_link

move_rate

move_speed

p_notice_death_c

p_notice_death_o

qual_bias

path_penalty_loc

path_penalty_risk

Default

0.0

1.0

0.5

0.0

0.1

0.0

1.0

0.0

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