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The Legal Grounds of Irregular Migration: A Global Game Approach



This paper analyses the relationship between regular and irregular migration taking into account the migration network effect and the network creation mechanism. We assume that migrants can obtain a high payoff only if a critical mass of migrants is reached in the destination country. If candidates to migration receive biased signals about the economic situation of the destination country, the migrants’ decision problem can be analyzed as a standard global game. Tying the quota of regular migrants to the economic performance of countries might create large discontinuities in immigration flows, with some countries attracting the bulk of irregular migrants and the other being shunned by the migrants.
March 3, 2017
The Legal Grounds of Irregular Migration: A Global Game Approach
Claire Naiditchand Radu Vranceanuy
This paper analyses the relationship between regular and irregular migration taking into account the
migration network e¤ect. We assume that migrants can obtain a high payo¤ only if a critical mass of
migrants is reached in the destination country. If candidates to migration receive biased signals about
the economic situation of the destination country, the migrants’ decision problem can be analyzed as
a standard global game. Tying the quota of regular migrants to the economic performance of countries
might create large discontinuities in immigration ‡ows, with some countries attracting the bulk of irregular
migrants and the other being shunned by the migrants.
Keywords: Irregular migration, Networks, Migration policy, Immigration quotas, Global games.
JEL Classi…cation: F22, C72, D84.
University of Lille, LEM -CN RS (U MR 9221 ), Cité Scienti…que, 59655 Villeneuve dAscq Cedex, France, E-mail:
yESSEC Business School and THEM A (UM R 8184), 3 Av. Bern ard Hirsch, 95021 Cergy, France, E-m ail:
1 Introduction
During the last four years, the European Union (EU) has been confronted with massive immigrant
in‡ows mainly from Syria and Afghanistan, as well as from Africa (Eritrea, Nigeria...). According
to the International Organization for Migration (IOM), more than a million migrants, most seeking
refuge, crossed into Europe in 2015, compared with just 280,000 the year before.1In 2016, the
organization recorded 390,000 arrivals. However, exact numbers are unclear as some may have
passed through borders undetected.2
This massive immigration phenomenon clearly took the European Commission (EC) and the
governments of the EU member countries by surprise. After hesitating several times, on May 13,
2015 the EU agreed on the European Agenda on Migration, which, in September 2015, led the
EC to adopt a "temporary relocation system". This system mainly targeted the 160,000 asylum
applicants who were in Greece and Italy at that time, and a resettlement agreement targeting
persons in obvious need of international protection was reached in July 2015. Distribution was
calculated according to several indicators of the host country: the size of its population, its total
GDP, its unemployment rate and its average number of asylum applications over the previous four
years.3The relocation plan has never been applied in its original framework, as it met a strong
opposition from the Visegrad group.4Lately, support for the relocation scheme has faded in the
remaining EU countries. One year later, the numbers of relocated migrants are falling short of the
initial quotas. The success of the Brexit motion in the June 2016 referendum which should lead
1The International Organization for Migration de…nes an international m igrant as any person who is movin g
or has moved across an international border, regardless of (1) the person s legal status; (2) whether the movem ent
is voluntary or involuntary; (3) what the causes for the movement are; or (4) what the length of the stay is. The
Convention relating to the Sta tus of Refugees (1951) as modi…ed by the 1967 Protocol de…nes a refugee as a p erson
who "owing to a well-founded fear of persecution for reasons of race, religion, nationality, membership of a particular
social group or political opinions, is outside the country of his nationality and is unable or, owin g to su ch fear, is
unwilling to avail himself of the protection of that country". A person awaiting a decision on the application for
refugee status under relevant international and national instruments is an asylum seeker.
2See the website of the International Organization for Migration at
3See : E uropean Com mission - Press release, Relocation and Resettlement: Increased e¤ orts on rese ttlement and
relocation must be sustained, Brussels, 15 June 2016, IP-16-2178_ en.htm
4Czech Republic, Hungary, Poland and S lovakia.
to the UK’s exiting the EU, was to a large extent fuelled by fears of "uncontrolled" immigration.
More intriguing, migrants themselves appear to be reluctant to comply with the EU relocation
targets, with a large majority aiming to reach highly attractive countries such as Germany and
the UK, while shunning other large countries such as France, which are no less able to welcome
Thus, the issue of migration is gradually turning into an issue of irregular migration, which
is much more di¢ cult to address using standard tools of migratory policy such as quotas, visas
and work permits. According to the IOM, “irregular migration”includes movements that take
place outside the regulatory norms of the sending, transit and receiving countries. In this paper,
we will adopt the perspective of the receiving countries, and refer to an “irregular migrant”as a
person who “enters, stays or works in a country without the necessary authorization or documents
required under immigration regulations”.6Depending on the context and the subtleties of the
legal language used, these migrants are sometimes referred to as undocumented, unauthorized,
illegal, clandestins (in French), etc. However, the IOM de…nition appears to be the most relevant
to this paper, which will contrast regular (or o¢ cial) ‡ows to irregular migration ‡ows. Irregular
migrants arrive without the approval of the national authorities of the receiving countries, and most
of the time they will try to hide from these authorities. In the case of the recent massive in‡ows
of migrants to the EU, most enter the EU irregularly.7Among these irregular migrants, some
do not claim refugee status and thus remain irregular migrants; others proceed to their preferred
destinations without complying with the Dublin Regulation (which determines the Member State
responsible for the examination of asylum applications; see Achilli, 2016 on Syrian asylum seekers);
5See for instance: The dispensable French, The E conomist, November 7, 201 5, ews/europe/21677987-france-has-less-and-less-in‡uence-eu-and-fears-use-what-it-
still-has-disp ensable. See also Refugees shun France, land of red tap e, unemploym ent and po or housing, The
Telegraph, Septemb er 21, 2015,
shun-France-land-of-red-tape-unemploym ent-and-po or-h ousing.html.
6As de…ned by the IOM, accessed on June 02, 2016: http://ww
7Migrant crisis: Migration to Europe explained in seven charts, BBC , March 4, 2016, /news/world-europe-34131911 and What happens to failed asylum seekers?, BBC News
Magazine, August 13, 2015, s/m agazine-33849593.
others apply for asylum but are not granted the refugee status and remain irregularly (either
because they do not return to their places or origin, are not removed and/or are de facto non-
removable; Clandestino, 2009). All these migrants are thus irregular migrants.
When choosing their …nal destination countries, these migrants make rational decisions under
imperfect information and intend to maximize their utility (Bilger et al., 2006). Today many of the
migrants who reach the EU do intend to claim refugee status, i.e. they ‡ed their countries of origin
to protect their lives and their freedom.8We can consider that their decisions as being made in
two-stages: …rst, they decide to escape their home country, where their lives are under threat and
travel to a neighbouring safe country; second, they choose their …nal destination. This second-
stage decision implies a comparison of expected incomes across the di¤erent possible destinations,
leading the migrants to decide whether they should choose a safe but less developed country over
a more developed one, and in the latter case, they must choose the developed country (within the
EU, for instance) in which they want to live.
A substantial body of literature has been devoted to analyzing the determinants of interna-
tional labour migration, from the classical wage di¤erential motive to more sophisticated theories,
emphasizing job search, risk diversi…cation and insurance for those remaining at home, credit con-
straints at home for the household, family reasons, etc. (see the recent literature review by Massey,
2015). Empirical studies have shown that the probability of preferring one country over another is
related to economic variables, to geography and culture, and to institutions in both the origin and
the destination countries (see for instance Hatton and Williamson, 2002; Mayda, 2010; Beine et
al., 2015). Several recent papers emphasize the migration network e¤ect (Carrington et al., 1996;
Munshi, 2003; Beine, Docquier and Ozden, 2011; Beine, 2013; Beine and Salomone, 2013), de…ned
as “the global in‡uence exerted by migrants at destination on the ‡ows of newcomers from their
origin country”(Beine, 2013). While these networks can di¤er in their size, structure, density and
8The Organization for African Unity Convention of 1969 expanded the de…nition of refugees to include not only
individuals subject to p ersecution, but also every p erson who "owing to external aggression, o ccupation, foreign
domination, or events seriously disturbing public compelled to seek refuge in anoth er place
outside his country of origin or nationality."
ectiveness, they all deliver “services” to newcomers, such as a culturally friendly environment
and an e¢ cient job matching mechanism, which helps migrants to …nd jobs. According to Beine
(2013), the elasticity of bilateral migration ‡ows related to the network e¤ect is approximately 0.4
and increases to 0.7 for migration to OECD countries.9
The recent massive in‡ows of migrants to the EU –and the associated policy challenges –
call for a careful investigation of the link between regular and irregular migration. This paper
emphasizes the "supply" complementarity between regular and irregular migrants, stemming from
the network e¤ect: essentially, increasing the number of regular migrants increases the network
size and thus facilitates migration for irregular migrants. Speci…cally, we assume that the network
operates e¢ ciently and allows to irregular migrants to get a high payo¤ only if a critical mass
of regular and irregular migrants is reached. The next section will review the relatively scarce
literature that analyses the relationship between the two types of migrants, and will present
existing research about the network e¤ect in the migration context.
In our model, South-North migration is fundamentally driven by economic motives. A mi-
grant’s decision-making problem can thus be represented as a coordination game with strategic
complementarities, where the migrant’s utility is strictly positive utility only if a critical mass of
migrants has made the same decision to migrate. In a destination country, there will be a number
of regular migrants that match the quota set by the government. The analysis focuses on the
decision of candidates to pursue irregular migration. We follow a growing body of literature that
demonstrated the applications of a particular equilibrium re…nement in coordination games and
consider that potential migrants have heterogeneous information about the destination economy;
more precisely, each of them receives a noisy idiosyncratic signal about the economic fundamentals
of the destination country. Thus, beliefs are no longer common knowledge, and the problem can
be analysed as a standard "global game" as pioneered by Carlsson and Van Damme (1993) and
9As explained by Beine (2013), the measures of diasporas in empirical studies are often u nderestimated since
most of the time, they in clude only regular and permanent adult m igrants.
extended to n-players by Morris and Shin (1998, 2001). In most of these games, players adopt
an equilibrium “switching strategy”, taking one course of action if they receive a signal above a
critical threshold, and another course of action if the signal is below the critical threshold. We
will show that, in this model as well, there is a critical signal above which individuals decide to
irregularly migrate, and below which they decide to stay in their origin country. Related to this
critical signal, there is a “cut-o¤ state of the economy” above which a critical mass of migrants
(regular and irregular) arrives and creates an e¤ective network and below which the network does
not reach the critical mass to operate properly. These critical thresholds are negatively related to
the number of regular migrants. Intuitively, the higher the quotas of regular migrants, the easier
it is for the network to reach the critical mass even if the economic situation of the country is not
very favourable; in turn, this prompts more irregular migrants to target that country.
Our model builds on several limiting assumptions. First, the model is “static” insofar as we
do not take into account the ‡ow of information transmitted by early migrants to subsequent
cohorts. As it is, it can represent of a one-shot massive migration episode essentially driven by
the economic motive. Second, in the economic literature, the network e¤ect is generally de…ned
as the increase in value of consuming a product if many other consumers use the same product
(Birke, 2009). In the context of migration, the network e¤ect would require that the individual’s
bene…t from migration is increasing in the number of migrants choosing to live in a destination
country. In this paper, we build our model according to the special case in which the positive
relationship between the bene…ts delivered by the network and its size is discontinuous; more
speci…cally, we assume that the network becomes operational if a critical mass of migrants is
reached, and will not function properly if that critical mass is not reached. If the critical mass is
reached, the migrant’s payo¤ is assumed to be proportional to the economic fundamentals of the
destination country. The model could be easily extended to a case in which the individual payo¤
increases with the number of migrants (Munshi, 2003), insofar as this number of migrants itself
depends on the economic fundamentals of the host country. Third, our analysis cannot address the
exclusion issue, where, above a given number of migrants, the migrant’s individual pay would
decline in the stock of migrants, for instance because the local attitude toward migrants changes
from support to fear and exclusion or the migration network is diluted in the native population
(Calvo-Armengol and Zenou, 2005). Thus, our model makes sense only if the number of migrants
is relatively low compared to the population of the destination country. Finally, in our analysis,
the bene…t of an e¤ective network is delivered to irregular migrants regardless of the networks’
composition of regular and irregular migrants. One can argue that regular migrants can help the
arriving irregular migrants more than the other irregular migrants. This is probably true when
considering housing and jobs in the formal sector. On the other hand, our assumption makes
sense if we agree that irregular migrants tend to …nd jobs in the informal sector, where networks
of irregular migrants might play a signi…cant role.
The following section introduces the related literature. Section 3 presents the assumptions of
the model. Section 4 solves the model for the equilibrium of the game and Section 5 concludes.
2 Related literature
The link between regular and irregular migration has only been studied by economists fairly re-
cently. As will be shown, a few papers emphasize the demand perspective in the host country, and
note the demand substitution between regular and irregular migrant labour. Other papers empha-
size the migrant supply perspective, where regular and irregular migrants can either complement
or substitute each other.
Taking a demand perspective, expanded legal possibilities for regular migration could decrease
the level of irregular migration, because the demand for low-skilled immigrant labour would be
lled by regular migrants instead of irregular ones. For instance, in his literature review on il-
legal migration from Mexico to the US, Hanson (2006) reveals that large-scale illegal migration
from Mexico to the US started at the end of the Bracero program (1942-1964), which allowed US
employers to hire Mexican and Caribbean workers on shirt-term contracts. Similarly, Ambrosini
(2010) argues that more restrictive migration policies in the EU led to an increase in the number
of irregular migrants (to satisfy the labour demand of host countries). This mechanism implicitly
assumes that the supply of regular and irregular migrants is in…nitely elastic, which is question-
able. Moreover, it also assumes that …rms hire irregular workers because of a shortage of regular
employees. However, such …rms may simply have a preference for irregular employees; increasing
the number of regular migrants would then have no impact on the number of irregular migrants.
In a theoretical model, Bchir (2008) demonstrates that the liberalization of the temporary move-
ments of workers could either lead to a decrease or an increase in irregular migration, depending
mainly on the quota of temporary workers and on their wages.
Turning to the supply of migrant labour, existing studies emphasize the complementarity
between the two types of migrants, intermediated by some type of network e¤ect. As already
mentioned, the network e¤ect re‡ects the higher facility to migrate in countries where the existing
stock of migrants of the same community is large. The reasons for this positive relationship are
multiple, ranging from the psychological utility of living in an environment that replicates the
culture of the country of origin, to “services”delivered by the community of similar individuals,
such as temporary aid, shelter or support in …nding a job (Mahuteau and Junankar, 2008; Epstein
and Gang, 2010). De Hass (2007) explains that migration networks not only decrease the material
and psychological costs of migration but also increase the exposure of potential migrants to the
relative wealth of international migrants, in turn increasing their perception of their own relative
deprivation and thus their incentives to migrate. Massey et al. (1993) even show that the network
ect may become so strong that the perpetuation of migration (regular as well as irregular) may
become almost uncorrelated with wage di¤erentials or employment rates in the origin and host
Several scholars argued that irregular migrants would bene…t more form the network com-
pared to regular migrants. Indeed, the latter can …nd jobs in the formal and informal sectors,
whereas irregular migrants can only access the informal sector and often …nd a job within their
communities, where labour networks play a crucial role (Ambrosini, 2010; Boyd and Nowak, 2012).
Irregular migrants usually do not bene…t from social services, which implies that they rely more
than regular migrants on their networks to maintain a decent standard of living (Collyer, 2005;
Williams, 2006). Boswell (2003) notes that increasing the number of regular migrants could raise
expectations about the labour market in the host country and would increase the size of the migra-
tion network, with both phenomena leading to an increase in irregular migration. Hanson (2006)
mentions that Mexicans with relatives in the US appear to have higher incentives to migrate ir-
regularly, either because they bene…t from the e¤ect of migration networks (lowering the cost of
migration) or because irregular migration increases their chances of becoming regular migrants
later on (increasing the bene…ts of migration). Bilger et al. (2006) argue that irregular migrants
are much more responsive to the network e¤ect than regular migrants who are backed by local
country policies and institutions (support income, education, job agencies, etc). Furthermore,
Broeders and Engbersen (2007) suggest that irregular migrants use informal migration networks
to avoid detection by the state and to remain in the shadows of ethnic communities. Finally,
irregular migrants bene…tting from large networks have a higher probability of settling regularly
(Hagan, 1998), which in turn increases their earning prospects.
These studies focus on the consequences of an existing network on the decision to migrate
(regularly or irregularly). This paper aims to contribute to this literature by emphasizing the
network creation process and the migrants’coordination decision problem, taking into account
the heterogenous structure of information. To our knowledge, this is the …rst time that the global
games analysis pioneered by Morris and Shin (1998, 2001) is applied to the migration problem.
3 Main assumptions
We study the dynamics of migration between two countries, a rich country from the North and
a poorer country from the South. The decision to migrate from South to North is driven by
economic reasons, with individuals aiming to maximize their expected payo¤.1 0
The North chooses the numbers of regular migrants L, according to its migratory policy.
Because these regular migrants reach the North through an o¢ cial programme, they will have
access to jobs and social security. Our analysis will focus on the fate and decisions of candidates
for irregular migration, which are excluded from the regular migration programme. Let Sbe
the pool of candidates for irregular migration, which, for simplicity, is assumed to be constant.
Candidates to irregular migration have similar personal characteristics; in particular, they are
risk-neutral individuals.11
Let us denote by the state of the fundamentals of the North economy, with 2[0;1], with
0being representative of a depressed economy, and 1of a booming economy. The better the
economic situation, the higher . This state of the economy is a random variable with a known
statistical distribution.
To introduce the network e¤ect a¤ecting the decision of irregular migrants, we assume, follow-
ing Massey et al. (1993), that there is a critical number of migrants V; above which the network
is created and operates properly. To rule out a trivial outcome, we consider that V < S: The
condition for the network to operate properly is thus:
Let us de…ne by m=M=S the frequency of actual migration in the mass of candidates to irregular
migration, with m2[0;1]:Then the network creation condition becomes:
mS +LV,m+lv(2)
with l=L=S and v=V=S; with v < 1:
10 T hus the model ap plies to asylum seekers, who are considering their secon d stage decision, where they must
choo se between a country close to their origin country, safe but not develop ed, and a develop ed country farther
away. It also applies to migrants w ho already reached the EU and are cho osing their destination country. In the
context of these decisions, we consider asylum seekers’ motives to leave as essentially economic.
11 T his simplifying assumption allows us to provide an analytical solution. T he problem could be extended to
allow for risk-averse or risk seeking m igrants by including a Von Neum ann - M orgenstern utility function. This more
general but also more com plex problem would entail sim ilar conclusions to those obtained under the assumption
or risk-neutrality.
We assume that the migration policy in the North can be expressed by a policy rule applied to
regular migration. A plausible policy reaction function that allows for simple future calculations
is l=: According to this function, the number of legal migrants (relative to S) is an increasing
function in ; representing the economic fundamentals of the North (Chiswick and Hatton, 2003).
The parameter 2[0;1] captures the “openness”of migration policies in the North. The network
creation condition can be written as:
m+ v: (3)
The possible payo¤s for an irregular migrant depend on his decision and the decisions of the other
potential migrants, which ultimately allow the network to reach the critical size. If he migrates
and the network operates properly, an irregular migrant can earn a positive income R, otherwise
he earns a subsistence amount that will be normalized to zero. If he decides to stay, he earns a
certain payo¤ s: These pays can be summarized as:
Migrates: 8
If: m+ v, then he gets R
If: m+ < v, then he gets 0
Stays: he gets s
The migration payo¤ Ris higher than s(R > s)and is increasing in the fundamentals of the host
economy, R=R():
To obtain closed form solutions, we need to be more speci…c about the information structure of
the problem. We assume that the “fundamentals of the economy”variable is uniformly distributed
in the [0;1] interval, i:e : unif[0;1].
Finally, potential migrants observe the realized economic fundamentals of the North with an
individual speci…c-bias. A migrant iwill thus observe the following signal: xi=+ei; we will
consider that signals are also uniformly distributed across migrants, with ei unif[; ], with
 > 0.
4 The equilibrium
In a perfect information setting (where would be common knowledge), we can distinguish between
two cases. If l= v, the network is created by regular migrants regardless of irregular migrants,
so any potential candidate for irregular migration should migrate, because he/she would obtain
the high payo¤ R: In equilibrium all candidates for irregular migration do migrate.
For l= < v, this coordination game with strategic complementarity features multiple
equilibria, a standard outcome of such coordination games. The …rst is the payo¤-dominant Nash
equilibrium. If all potential migrants leave their origin countries (m= 1), then l+m1> v;
the network is created and all irregular migrants obtain R. An individual who would unilaterally
deviate and choose the “stay” strategy would regret it, because s<R. However, because this
payo¤-dominant equilibrium relies on the decision to migrate by all other candidates for migration,
it is subject to “strategic uncertainty”. Should candidates for migration fail to coordinate their
actions (migrate), they could end up with a zero payo¤. In the second Nash equilibrium, candidates
for irregular migration coordinate with regard to the “stay”strategy (m= 0); they all obtain the
certain positive payo¤ swithout incurring the strategic risk. The individual who would deviate
unilaterally and migrate would obtain zero, because the critical threshold (v)is not reached.
While multiple equilibria might have an appeal to theorists, they have little utility for policy
analysis insofar as one cannot predict the consequences of changes in policy parameters if he cannot
de…ne what the equilibrium of the system is. One relevant equilibrium re…nement for coordination
games with strategic complementarities was introduced by Carlson and Van Damme (1993) in the
2-player case and was extended to the n-player case by Morris and Shin (1998, 2001). In their
analysis, information is “heterogeneous”- agents do not observe the fundamentals of the economy
(), but rather receive a biased signal of its state, with each individual receiving his own signal.
In this context, beliefs are no longer common knowledge and agents cannot perfectly coordinate
their actions. This “small”change in the structure of information can eliminate the multiplicity of
equilibria and replace it by a single equilibrium of a special form. Indeed, these problems present
a so-called “threshold equilibrium”de…ned by a unique critical signal xaround which individuals
switch strategies.
In the migration context, it can be shown that there is a unique critical signal xsuch that
individuals receiving a signal xxmigrate (irregularly), and those receiving x < xstay.
Related to this signal, there is a unique cut-o¤ state of the economy below which the number of
residents of the South who decide to migrate irregularly is too small to reach the critical threshold
v; and vice-versa. For the sake of parsimony we do not recall here the formal proof of existence of
the threshold equilibrium as developed by Morris and Shin (2001) which proceeds by successive
elimination of dominated strategies. Instead, we …rst assume that these thresholds exist and prove
that they are unique. The resolution steps follow Atkeson (2001).
4.1 The cut-o¤ state of the economy
According to our assumptions regarding the distribution of the errors, when Nature draws a state
of the economy , signals xiwill be uniformly distributed on [();(+)] among the population
of potential migrants.12 For any given critical signal x, the frequency of irregular migrants is
an increasing function in :
m() = Pr [xixj] = 1
We de…ne the cut-o¤ state of the economy as the fundamentals’ value for which the critical
mass of migrants vis reached; that is, if , then  +mv(the migration episode succeeds)
and vice-versa.
Because mis an increasing function of , the implicit de…nition of the cut-o¤ state of the
economy for a given xis:
m() + =v,x+= 2(1 v+)(6)
12 We fo cus here on the case where is small. In the general case, the sup port of the distribution is
unif [max [0;()] ;min [(+);1]] :
4.2 The critical signal
We now look for the critical signal x, characteristic of the individual who is indi¤erent between
staying and migrating. According to the de…nition of , the migration episode succeeds in creating
the e¢ cient network for , and fails if  < . The indi¤erent migrant’s expected gain is as
E[Rj] = ZS
R()f(jx)d (7)
where f(jx)is the ex-post distribution of for the individual with signal xand Sis the upper
bound of the ex-post distribution.
Given the assumption of the uniform distribution of the signals, for the migrants who receive
the signal x;the ex-post distribution of is unif [(x);(x+)]. In this case, the ex-post
density is f(jx) = 1=(2)and the upper bound is (x+). Thus, we can write the expected
gain of the indi¤erent individual as follows:
E[Rj] = 1
R()d (8)
To obtain an analytical solution, we make the simplifying assumption according to which the
migrant’s pay in the event of the success of the migration episode is linearly increasing in :
R() = s+a (9)
with a > 0a parameter.
Under this assumption, the expected gain can be calculated as follows:
E[Rj] = 1
2s + 0:5a2(x+)
4(x+) [2s+a(x++)] (10)
The indi¤erence condition s=E[Rj]implicitly de…nes the critical signal xfor a given :
4(x+) [a(x+) + 2(a+s)] = s(11)
An individual iwho gets a signal xi> xwould expect a gain higher than s; and vice-versa.
4.3 The equilibrium
We can solve the system of two equations (6) and (11) and two unknowns (; x) for the joint
(equilibrium) solution. In so doing, we replace x+= 2(1 v+)in Eq. (11) to obtain
a quadratic equation de…ning :
(1 v+) [a (1 v+)+(a+s)] = s(12)
The equilibrium cut-o¤ state of the economy depends on the parameters of the problem: =
(a; s; v;  ; ).
The equation (12) has at most one positive root, and this requires that sv
a(1 v)2, i.e., if
the “noise”in the signals is not too large. The solution is:
=q[s +a(1 v)]2+ 4 sa (v+)[s +a(1 v) (1 + 2)]
2a (1 + )(13)
Equation (6) then allows us to determine the critical signal x=x(a; s; v; ; ):The actual
frequency of irregular migrants m(in the population S)is a function of the actual and the
equilibrium critical signal x:m() = Pr [xixj] = fmax(0;1
2[(+)x]); min(1;1
If the noise in the information ‡ow is high, more precisely if  > sv
a(1 v)2, then Equation
(12) has no positive root. Thus, whatever 2[0;1] we have  > : whatever the state of the
economy the critical migration threshold is reached; m= 1;a large ‡ow of irregular migration has
to be expected.
As shown by Morris and Shin (1998, 2001), global games present an interesting limit case
when the variance of private information tends to zero without fully suppressing the imperfection
of information (see also Heinemann et al., 2009). For !0, the equilibrium cut-o¤ state of the
economy can be written as follows:
[]!0=q[s +a(1 v)]2+ 4sav [s +a(1 v)]
2a >0(14)
and the critical signal becomes x=. In this special case, the threshold equilibrium still
prevails; the migration decision depends on the economic situation of the host country (almost
known to the migrants): if , all candidates for irregular migration receive signals above x
so m= 1, and if  < ; m = 0.
4.4 Properties of the equilibrium
In what follows, let us focus on the most interesting case where is small enough, such as >0
and (x)>0:The set of for which 0m()1is the interval [(x);(x+)]; on this
interval, mis a linear, increasing function in : For lying outside of the interval [(x);(x+)];
candidates for irregular migration will either all migrate or all stay:The smaller is, the narrower
this interval. When tends to zero, the regime shift from m= 0 to m= 1 is the most brutal, or
the model presents the strongest "discontinuity".
For >0, when Nature chases  < , the high migration payo¤ is not reached, and indi-
viduals who get a signal above the critical signal and migrate irregularly will end up in a worse
situation compared to staying in their origin country. In this case, the chances that the critical
migration threshold () is reached are measured by Pr[ > ] = 1 .
We can now study how the cut-o¤ state of the economy and thus the tendency to attract
irregular migrants varies with the parameters of the game, particularly with the noise of the
signals and the openness to migration. The total derivative of expression (12) allows us to see
that is decreasing in ,and a, and increasing in v:
d =a[1 v+]2
a(1 + 2) (1 v+) + (a+s)<0
d =[2a (1 v+)+(a+s)]
a(1 + 2) (1 v+) + (a+s)<0
da =(1 v+) [(1 v+) + ]
a(1 + 2) (1 v+) + (a+s)<0
dv =2a (1 v+)+(a+s)
a(1 + 2) (1 v+) + (a+s)>0
ds =v
a(1 + 2) (1 v+) + (a+s)>0
First, the critical cut-o¤ state of the economy is decreasing in the noise of the signals. Thus,
the higher the noise, the higher the range of leading to high irregular migration. In the model,
this can be easily rationalized. When noise is high in a given state of the economy, more can-
didates for migration will receive high signals and decide to migrate. In turn, this higher ‡ow
of migrants guarantees that the critical network threshold is reached even if the fundamentals
of the economy are poorer. In the current EU migration crisis, one important culprit is the de-
gree of migrants’misinformation about the opportunities each countries can o¤er, misinformation
sometimes fuelled by tra¢ ckers (Schloenhardt, 2002 studying the smuggling of migrants in the
Asia-Paci…c region; Bilder et al., 2006 studying human smuggling to Austria). For this reason,
several EU countries (such as Denmark and Norway) have …nanced information campaigns in
migrants’origin countries.13
Second, if the host country becomes more open to regular migrants (increases), the critical
threshold vcan be reached more easily, and the chances that the migration episode for irregular
migrants succeeds also increase. Thus, an increase in would both increase the ‡ow of regular
migrants and the attractiveness of the country for irregular migrants.
In line with intuition, if the marginal bene…t of migration (a) increases, chances that the
migration episode succeeds increase; if the critical migration threshold (v) is increased, chances
that the migration episode succeeds decline. The sign of d=ds is the same as the sign of (v);
which must be positive.14 While a higher sincreases both the payo¤ in the “stay”equilibrium (s)
and the high payo¤ in the risky “migrate”equilibrium (R() = s+a), the former e¤ect applying
to the whole mass of candidates for irregular migration appears to take over the latter e¤ect.
Finally, all other variables kept constant, Mand Lvary jointly depending on the shocks to
13 N orway launches anti-refugee advertising campaign, The Telegraph, Novem-
ber 4, 2015, http://www
launches-anti-refugee-advertising-campaign.html, and Denmark pu ts ad in Lebanese news-
pap ers: Dear refugees, don’t com e here, The Washington Post, September 7, 2015,
https://w ww.washingtonp /news/worldview s/wp/2015/09/07/denm ark-places-an-advertisement-in-
lebanese-new spapers-dear-refugees-dont-come-here/.
14 If l=> v ; legal migration su¢ ces to create the network, thus all candidates for irregular migration should
migrate regardless of their sign als.
economic fundamentals of the destination country (realized values of ):We recall the expressions
of the numbers of regular and irregular migrants, L=S and M=m()S: A large would
prompt authorities in the North to accept more regular migrants, dL=d > 0and will also raise the
proportion of irregular migrants, thus dM=d > 0:In this model, regular and irregular migration
have a positive covariance, driven by the random realization of : One important initial assumption
consisted in considering the number of candidates to irregular migration Sas constant. Implicitly,
we assumed that candidates to illegal migration do not qualify for the regular migration policy of
the North. In an alternative, more complex model, any additional regular migrant might reduce
the number of potential irregular migrants by one. In this case, a higher proportion of migrants
would apply to a reduced pool of potential irregular migrants, with a positive or a negative e¤ect
on the total number of irregular migrants.
5 Conclusion
In this paper, we build a small model to analyse the interaction between the number of regular
migrants as resulting from the migration policy of a "rich" country and the in‡ow of irregular
migrants. This analysis acknowledges the essential role of the migrant network on the decision to
migrate irregularly as revealed by several studies surveyed in the Introduction. It contributes to
this literature by analysing the network creation process in the context of migrants’heterogenous
information about the host country. The decision problem of potential migrants is formalized as
an n-player global game, in line with the classical analysis by Morris and Shin (1998, 2001). We
solve the migrant coordination game for the threshold equilibrium. Like many other global games,
this one presents an equilibrium cut-o¤ state of the economy above which the “rich”country will
be subject to high irregular migration, and below which irregular migrants will not target the
Under the assumption of a constant pool of candidates to irregular migration, the analysis
revealed a positive correlation between the number of regular migrants and the number of irregular
migrants, driven by ‡uctuations in the economic fundamentals variable. It further shows that a
policy allowing high numbers of regular migrants can make a country more appealing to irregular
migrants even if the economic outlook is less favourable. Finally, the model shows that reducing
the information bias of potential migrants would reduce the probability of attracting substantial
irregular migration.
In the context of the recent EU challenge of massive immigration ‡ows, the question of how the
quota of regular migrants (including asylum seekers and refugees) is determined becomes a crucial
issue because it also determines the number of irregular migrants. Irregular migrants, given the
very de…nition of the concept, cannot be allocated because they are not observed as such and are
not supposed to exist.
Our analysis has shown that simply tying the number of regular migrants to the economic
outlook of a country can entail large discontinuities in the in‡ows of irregular migrants, with
countries with a good economic outlook attracting most of the migrants, while countries with a
poor economic outlook are shunned. This is probably one original …nding of our analysis, that the
frontier between what makes a country attractive / unattractive for massive irregular migration
relies on small variations in exogenous variables such as the state of the economy or the quota of
legal migration. This positive / negative ampli…cation results from the income factor compounding
its e¤ect on the network e¤ect, which is the consequence of the threshold equilibrium. The higher
the precision of the signals, the stronger the discontinuities in the migration ‡ows; in the absence
of tight border controls, some countries might attract all of the irregular migrants.
When deciding how many regular migrants (asylum seekers or refugees) it allocates to a coun-
try, the EC must take into account the indirect consequences of this policy on the number of
irregular migrants this country will attract, for instance by providing material support to these
countries that goes beyond support for regular migrants only. In countries with a modest economic
outlook, high irregular migration may be the outcome of high noise in the signals; the EU could
also …nance information campaigns in migrants’origin countries, informing them about the true
conditions of irregular migrants in the destination country, and encouraging them to follow only
the regular channels to migration.
Acknowledgement 1 The authors are grateful to two anonymous referees as well as partici-
pants to the 5th Lille-Ghent Workshop in Economics, Gand (Belgium), Dec. 2015, the Annual
Conference of the International Trade and Finance Association, Sarasota (Florida, USA) Mai
2015, Séminaire Equippe - Economie, Lille (France), Dec. 2014, the Wim Meeusen Workshop,
Santander (Spain), Oct. 2014, for their suggestions and comments that helped them to improve
the quality of the paper. Radu Vranceanu carried out this research within the framework of the
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