FUNDAC
¸ ˜
AO GETULIO VARGAS
ESCOLA DE P ´
OS-GRADUAC
¸ ˜
AO EM ECONOMIA
Pedro Brand˜ao Solti
Foreign Support, Internal Political Disputes and Mass
Killings
Rio de Janeiro
Pedro Brand˜ao Solti
Foreign Support, Internal Political Disputes and Mass
Killings
Dissertac¸˜ao submetida a Escola de
P´os-Graduac¸˜ao em Economia como requisito
parcial para a obtenc¸˜ao do grau de Mestre
em Economia.
Orientador: Lucas J´over Maestri
Rio de Janeiro
Ficha catalográfica elaborada pela Biblioteca Mario Henrique Simonsen/FGV
Solti, Pedro Brandão
Foreign support, internal political disputes and mass killings / Pedro Brandão Solti. - 2016.
33 f.
Dissertação (mestrado) - Fundação Getulio Vargas, Escola de Pós-Graduação em Economia.
Orientador: Lucas Jóver Maestri. Inclui bibliografia.
1. Economia. 2. Genocídio – Aspectos econômicos. 3. Negociação. 4. Guerra civil. 5. Assistência econômica. I. Maestri, Lucas Jóver. II. Fundação Getulio Vargas. Escola de Pós- Graduação em Economia. III. Título.
Abstract
This paper studies the incentives underlying the relations between foreign coun-tries and rival domestic groups. It models the interaction in a infinitely-repeated game between these three players. The domestic groups bargain for a split of the domestic surplus and may engage in violent dispute for power and in uni-lateral mass killing processes. The foreign country may choose to support one of these groups in exchange for monetary transfers. The paper characterizes the parametric set in which strategies leading to no violent disputes nor mass killings are Subgame Perfect Nash Equilibra in the presence of foreign support, but not in its absence.
KEYWORDS:Political Economy, Mass Killings, Bargaining, Civil War, Foreign Sup-port
Contents
1 Introduction 6
2 Related Literature 9
3 The Model 12
4 Equilibrium Analysis and Results 15
a Welfare Analysis . . . 20
5 Concluding Remarks 22
A Appendix 26
1
Introduction
History of mankind has seen uncountable episodes of mass genocides. They vary
in scope and motivation. Quite often, civilian deaths account for a large fraction of
the overall casualities. Since World War II, between 12 and 25 million civilian deaths
happened due to mass killings in war theaters as varied as Sudan, Myanmar, North
Korea and the Middle East1. These humanitarian crisis were driven by different sorts
of economic, cultural and political motivations.
It is very common for violent disputes for power between rival domestic groups to
end up dragging foreign countries to the confrontations, either directly or indirectly.
For instance, during the Cold War, both the United States and the Soviet Union used
to sponsor groups across the world to mantain political, economical and ideological
influence on their countries. Some well-known examples include the Soviet support
for Cuba and the US support in Nicaragua.
Since World War II, most interventions due to humanitarian concerns were
cen-tralized under the United Nations Peacekeeping program, which started as observing
forces in truces between different countries (Israel vs. Arab states; India vs. Pakistan),
but soon started interfering in internal disputes, such as in Congo in 1960. Still, many
of the foreign intermeddlings happen outside the realm of the United Nations. One
of the most famous episodes is, of course, the US intervention in Iraq, in 2003, but
it is not the only one. A few of the most recent examples include the Saudi military
action in Yemen, the Russian military action in Georgia and French military action in
Mali. The Middle East alone features an extremely complex network of foreign
sup-port from governments to different groups throughout the region2.
Military support does not come only in times of war. The United States Army’s
Foreign Military Financing fund has been sponsoring over 60 different countries in
1Source: Political Instability Task Force (2010)
2Some examples include Iranian support for Hezbollah, the Syrian government and Shia groups
the last few years, with a budget of approximately 5.7 billion US$ in 20143.
Colom-bia, Egypt, Israel, Jordan and Pakistan were, in 2008, the five biggest receivers of
for-eign military aid from the United States. All of those countries were facing domestic
threats to the incumbent governments, such as ethnic minorities (Palestineans in
Is-rael), religious extremists (Egypt, Jordan and Pakistan) or guerrilla groups (FARCs in
Colombia). The United States government opted to support the local governments,
according to US Department of State (2007), to “strengthen the security of the United
States and to promote peace in general”.
Another example is the French military support to its former Subsaharan African
colonies. The French government has signed many agreements with the incumbent
government of its former colonies in which they offer military support in case of
foreign threat. Nevertheless, as Guinant (2013) notes, there are many confidential
clauses that are widely perceived as offering military assistance in case of domestic
uprising. Collier et al. (2009) find that being a former French Subsaharan African
colony has a statistically significant negative effect on the likelihood of the country
facing civil war.
As Esteban et al. (2015) argue, internal mass killings and disputes for power are
quite often motivated by material reasons. We argue that it also may be the case for
foreign military support. In particular, why should the country spend resources in
military support to a foreign government during peaceful times? In this thesis, I
ex-tend Esteban et al. (2015)’s model by including a foreign power that exchanges
mili-tary support for economic advantages (namely direct transfers) and analyse whether
this influence may avoid mass killings inside the country.
This paper introduces a game-theoretical model played in infinite periods
be-tween three players: a foreign power and two rival domestic ethnic affiliations. The
foreign power offers military assistance in exchange for monetary transfers to one of
the ethnic groups, that may accept it or not. In the beginning of each period, one
of the groups is in power. The incumbent group makes a take-it-or-leave-it offer
on the split of the surplus, and if they do not reach an agreement, they dispute for
power. Military support increases the probability of winning this dispute. In the end
of the period, the group in power chooses whether or not to commit ethnic cleansing
against its rivals, and the supported group and the foreign power decide whether or
not to continue the military support.
Our first results suggest that, if the foreign power decides to support one of the
rival groups, than it supports the one originally in power. What drives this results
is the ability of the government to choose how much of the rival population will be
killed. If the foreign power were to support the opposition, the incumbent group
could promote an ethnic cleansing to undo this military aid. Above that, as the
in-cumbent group is not subject to any sort of commitment device (international law,
for example), there is no possible off-equilibrium strategy that the other players may
use to punish him if he decides for mass killings.
Second, we characterize a set of parameters in which there is no Subgame Perfect
Nash Equilibria with no mass killings nor violent disputes for power in the absence of
foreign support, but there can be in its presence, depending on the cost function of
the military support. With foreign support, incumbent groups are so likely to win any
domestic disputes that the opposition has little incentives to rebel, losing leverage in
the bargaining process. The incumbent country gains bargaining power, relaxing its
incentive constraint and making it easier for peaceful equilibria to be enforceable.
The paper is organized as follows: in section 2 we discuss the papers that relates
the most to this one, specially Esteban et al. (2015); in section 3 we present the model;
in section 4 we analyse equilibria and present the main results, and section 5
2
Related Literature
The paper that most closely relates to ours is Esteban et al. (2015). In that paper,
the authors introduce by the first time in the literature a political economy model in
which interactions between two different rival groups in a country may lead to
eth-nic cleansing. They develop a simple model, in which one of the groups hold power,
they bargain for a split of the national surplus, and if the offers are not accepted, they
engage in civil war. The group that holds power may opt for mass killings of the
op-posite group as a way of gaining relative strength, despite the negative effects that it
may have on total surplus. They find that any Subgame Perfect Nash Equilibria in
sit-uations in which the domestric country: (i) relies too much on natural resources, (ii)
has a low labor productivity and (iii) has large asymmetries in the size of the
differ-ent groups cannot induce a path with no mass killings nor violdiffer-ent disputes for power.
Esteban et al. (2015) abstract from any interactions between rival groups and
for-eign actors, whilst in reality external powers very often play big role in the economies
and internal politics of countries. If they find that countries that rely heavily on
natu-ral resources are more likely to witness ethnic cleansings, these countries are usually
big commodity exporters, and may play decisive roles on the market of goods such
as petroleum or diamonds, for example.
In this thesis, I add a new player to the model of Esteban et al. (2015), called
for-eign power. Its role is to give supportαto one of the rival groups in exchange for a
money transfer. This support changes the balance of power in internal disputes. In
Esteban et al. (2015), group j defeats group i in a civil war with probability Nj
Ni+Nj,
in which Nℓ is the population size of group ℓ. Now, receiving foreign support α,
group j wins disputes with probability αNj
Ni+αNj. This modifies the barganing power
between countries and thus the incentives to mantain peace or engage in wars and
mass killings.
This paper is also related to a very large literature on civil wars. This literature
Blattman and Miguel (2010). In specific, there is a prolific empirical literature on the
effects of foreign influence in violient domestic disputes for power. Nunn and Qian
(2014) find that, on average, food aid promotes civil conflict, whereas de Ree and
Nillesen (2009) find that foreign aid has a negative effect on the duration of ongoing
civil wars.
Most of the political literature studying foreign aid and its relations to civil wars
focus on humanitarian aid. To the extent of my knowledge, Dube and Naidu (2015)
is the only paper that directly studies military aid. It analyses how American support
towards Colombian army affect local violence. They find that US aid is positively
correlated with attacks by paramilitary groups (known to work with the Colombian
military against guerilla groups), and negatively correlated with voter turnout. This
is particularly strong in villages close to Colombian military bases.
Collier et al. (2009) propose and test a ‘feasibility hypothesis’: if rebellion is
fea-sible given the priors of the economy, than it will happen. They empirically look for
the variables positively correlated with the probability of civil wars. In this paper, we
take a different position: whenever mantaining peace is Subgame Perfect Nash
Equi-librium, peace is enforced. Besides that, Collier et al. (2009) also find that a dummy
for former Subsaharan French colonies has a very statistically significant negative
ef-fect on the chances of civil wars erupting.
According to Guinant (2013), the French Republic has several cooperation treaties
with African countries on military cooperation, that include protection against
for-eign threat. Even if there are no explicit clauses on intervention in case of
domes-tic uprise, she argues that there are confidential clauses (to which not even French
deputies have access) that are believed to offer French support in domestic disputes.
French intervention in Mali starting in 2012 suggest that this may be true. We
pro-pose an explanation to that phenomenon by analysing how foreign aid affects
in-ternal political bargaining, and we find that it makes it more likely for peace to be
Grossman (1992) develops a general equilibrium model relating foreign aid,
re-source allocation, income inequality and insurrection. There are peasants and a
ruler. The ruler wants to satisfy its clientele. To do so, it can choose to tax or
sub-sidize the production of the peasants, and to hire them as soldiers. Foreign aid is
seen as a gift to the ruler, relaxing its budget constraint. Peasants allocate their labor
between production, soldiering and insurrection in order to maximie their income.
In case of succesful uprising, national income is distributed according to each
house-hold’s contribution to the revolt. In equilibrium, the increase in foreign aid creates
an incentive for the ruler to reduce taxes (or increase subsidies) and demand more
soldiering in order to deter peasant uprising. On the other hand, peasants allocate
more of their labor to insurrections to strengthen their claims for more resources.
Besides that, foreign aid reduces peasants’ share of national income.
Besley and Persson (2011) develop a game-theoretical model in which two groups
dispute for power in a country. In the beginning of each period, both groups choose
the size of their armies. The dispute is solved via a contest function. The winning
group determines spending on transfers, public goods and its army. The incumbent
group’s transfers are spent on consumption, whereas the opposition is split between
consumption and military investments. They find that there are three possible types
of equilibria: one in which noone invests in violence (peaceful equilibria), one in
which only the incumbent group invests in violence (repressful equilibria), and one
3
The Model
Our model is closely related to the one developed in Esteban et al. (2015). It is a
dynamic game, with infinite periods. There are three different players: two different
ethnic affiliations (henceforth called groups i and j) that cohabit the same
coun-try, and a foreign power. One of the ethnic affiliations starts holding the power in
its country. Each groupℓhas a population size of Nℓ, and in the beginning of each
period, surplusS = R+β(Ni+Nj)is produced, in whichRis a fixed income
repre-senting the country’s natural resources, anβis a labour productivity parameter.
The stage game develops as below:
(i)In periodτ = 0, the foreign power chooses one of the two ethnic groups and makes an offer: it gives a military aid ofαin exchange of a transfert. Once the offer
is made, it is up to the chosen group to accept it or refuse it. If it accepts, the foreign
power supports him with strengthα ≥ 1. If it refuses, the game follows withα = 1
andt = 0. Ifτ >0, the stage game starts in step(ii).
(ii)The group in power makes an offer to the other group on how to split the sur-plus.
(iii)Both groups decide on whether go to civil war or not. If both countries decide not to go to civil war, the incumbent’s offer is enforced. If at least one country
de-cides for civil war, they engage in confrontations, making the total surplus diminish
byd, thus becomingS−d. If countryℓhas foreign support, it wins the civil war with
probability αNℓ
αNℓ+N−ℓ
, and if it does not has foreign support, with probability Nℓ
Nℓ+αN−ℓ
.
Whoever wins this dispute holds power in the country and remains with the totality
of the surplusS−d.
(iv) Regardless of the country having faced civil war or not, both the supported group and the foreign power decide whether to mantain its relations or to end them.
still valid for the next period. If at least one of the players decide to cancel relations,
no transfers are made and support is withdrew. Once there is a rupture in the
part-nership between the foreign country and the previously supported group, it cannot
be restablished any more.
(v)The group holding power chooses a quantityM of the rival group to extermi-nate, such that in the next period, the rival group total population is N−ℓ −M. By
reducing the rival population size, the incumbent group increases its probability of
winning any future dispute for power, but reduces country’s surplus. In the end, each
group consumes what they have and enjoy utilityU(c) =c.
Formally, mayhorf be the information set of the foreing power when it decides the offer it makes to one of the rival ethnic groups andhτ
fbe its information set in the step
(iv)of periodτ. May⊔represent the concatenation of two vectors. Definehorf ={ℓ0};
h0
f = horf ⊔ {((α, t, k), q), λ0,{m0i, m0j}, ℓ1} and hτf = h τ−1
f ⊔ {{n τ−1
S , n τ−1
F }, Mτ
−1
, λτ,
{mτi, mτj}, ℓτ+1}, in which: (α, t, k)is the offer made by the foreign country (the triple stands for the amount of military support, the transfers due and the group being
of-fered, respectively);qis the acceptance or rejection of the offer by the ethnic group;
λτ the offer made by the incumbent group; {mτ
i, mτj} the decision to either engage
in dispute for power or not; ℓτ represents the ethnic group in power in the begin-ning of period τ; nτ
F and nτS represent the decision in periodτ by, respectively, the
supported group and the foreign country to mantain or not the partnership; andMτ
the amount of population killed in period τ. May Hτ
f be the family of all possible
information sets in stage (iv) of period τ, and Hf = {i, j} ∪ ∪
∞
τ=0Hτf the family of
all possible information sets. Therefore, the foreign country’s strategy is a function
σf :Hf →[1,∞)∪R+∪ {i, j} ∪ {continue, stop}∞4. The strategy of the ethnic groups
is a little more complicated to write down formally, since it depends on whether it is
supported or not, if it starts the period in power or not and if it ends the period in
power or not. I will refrain from specifying it for readability reasons.
4I suppose that the foreign power’s strategy set is very na¨ıve, in the sense that, in principle, it could
offer one of the ethnic groups a sequence of doublesQ
τ(ατ, tτ)in case it keeps paying the transfers,
The payoff of the foreign country is given byUf(σf, σi, σj) = P
∞
τ=0δτ tτ−c(ατ)
in
whichtτ is the transfer it receives in periodτ andατ measures how much support it gives in periodτandc(·)is the cost function for military aid. I suppose thatc(1) = 0,
c′
(α) ≥ 0and c′′
(α) ≥ 0for all α ≥ 1. Notice thatατ may either beαchosen by the foreign country atτ = 0or 1 in case it has its offer denied or it decides to withdraw
support. The payoff of the etnhic groups is the discounted flow of resources they
4
Equilibrium Analysis and Results
In Esteban et al. (2015)’s model, there is no foreign power. The surplus function,
the bargaining process and the power dispute contest function are exactly the same,
ifαis fixed as 1 andtfixed as 0. In their analysis, they first look for the worst possible
SPNE for the incumbent country, so that it can be used as an efficient off-equilibrium
punishment. They find that the worst SPNE always is a strategy profile in which both
groups always decide for war in every period they have a strictly positive population,
and the winning party decides to fully exterminate its rivals whenever it is possible.
Then, they characterize the necessary incentive constraints for a strategy with no
political disputes nor mass killings to be SPNE. They find that it is only possible if the
following restriction is met:
R ≤δβNj−(1−δ)[β(Ni+Nj)−d]
In this paper, we show that, by adding a new player, theforeign power, with the
ability to militarily assist one of the groups, it is possible to find SPNE with no mass
killings nor internal disputes for economies that do not respect the restriction above,
depending on the cost function of the foreign aid. For that, the following definition
may be useful throughout the article:
Definition 1. Apeaceful equilibrimis a Subgame Perfect Nash Equilibrium in which, in the equilibrium path, both groups always decide for the enforcement of the split
proposed by the incumbent, and the incumbent never makes mass killings. Using
the notation established before,{mτ
i, mτj}={peace, peace}andMτ = 0for allτ ∈N.
As in Esteban et al. (2015), the first step is to find the worst possible SPNE in order
to design efficient punishments. For that, we will first look to the subgame starting
int = 0, right after one of the groups either accepts or rejects the offer made by the
foreign country. Intuitively, as civil war diminishes surplus byd, one can expect that
in the worst equilibria civil war happens as frequently as possible. Besides that, due
to simultaneity in the declaration of civil war, there is always an equilibrium in which
The same argument applies to the decision to either continue or not the
assis-tance. There are always equilibria in which both the supported group and the foreign
country decide for the interruption of the relations between them. This can be seen
as a possibility of punishing the supported group in case it deviates, since, once it
had accepted the deal when offered, it is (weakly) better for him to keep the support.
It is important to understand what are the incentives for mass killings in the
equi-libria with the features described as above. In the appendix, we show that the
win-ning side always have incentives to promote total ethnic cleansing (that is, winwin-ning
group ℓ setsM = N−ℓ). This happens because the gains with future surplus never
compensate for the risk of losing the dispute in the next period and being itself the
subject of total mass killings.
The worst SPNE is, therefore, the strategy in which both groups always dispute
for power and promote total extermination of their rivals whenever possible, and the
supported group and the foreign power cancel the exchange of aid for transfers in
the first opportunity to do so. This is an SPNE and its payoff is always reachable to
any group.
Lemma. 1.The strategy profile consisting of both ethnic groups always disputing for
power and promoting mass killings after winning it, whereas the supported group
and the foreing power put an end to the military foreign support in the first possible
opportunity, is the worst SPNE of the subgame starting after the refusal or
accep-tance of the foreign power proposal in periodτ = 0.
Proof. See Appendix.
Having the most efficient punishment, we can check whether groups may have
incentives to deviate from a peaceful strategy. As the bargaining process is a
take-it-or-leave-it one, in which the incumbent group makes the offer and the opposition
either accepts or rejects, in equilibrium the incumbent group will either make an
of-fer that makes the opposition indifof-ferent between accepting or not, or it preof-fers to
equilibrium then the first case must be true.
Then, one necessary restriction for the peaceful strategy to be an equilibrium is
that the net surplus after the transfers to the foreign group (in case it is supported)
and to the opposition must be greater or equal to the expected payoff it gets from
disputing for power and perpetrating ethnic cleansing in case it wins. This
restric-tion can be written as below:
In case the supported group is the incumbent one:
1 1−δ
n
S−t− Ni
Ni+αNj
h
S−d− δ
1−δ(S−βNj)
io
≥ αNj
αNj+Ni
h
S−d+ δ
1−δ(S−βNi)
i
The left-hand side of the equation is the expected present value of the discounted
flow of payoffs that the incumbent country gets in a peaceful equilibrium. It remains
with the economy’s surplus, descounting the transferstto the foreign country and
the transfers Ni
Ni+αNj
h
S−d− δ
1−δ(S−βNj)
i
to the opposition group. This last
expres-sion is exactly the payoff that the opposition group would get by rebelling. The right
hand side is the expected present value of the discounted flow of payoffs that the
in-cumbent would get by disputing power. In case it wins, it would getS−din the first
period andS−βNiin the following ones.
In case the supported group is the opposition one:
1 1−δ
n
S− αNj
Ni+αNj
h
S−d− δ
1−δ(S−βNj)
i
−to≥ Ni
αNj+Ni
h
S−d+ δ
1−δ(S−βNj)
i
The left-hand side of the equation is the expected present value of the discounted
flow of payoffs that the incumbent country gets in a peaceful equilibrium. It remains
with the economy’s surplus, descounting the transferstto the foreign country and
the transfers αNj
Ni+αNj
h
S −d− δ
1−δ(S−βNj)
i
−tto the opposition group. This last
expression is exactly the payoff that the opposition group would get by rebelling. The
the incumbent would get by disputing power. In case it wins, it would getS−din the
first period andS−βNj in the following ones.
A second necessary restriction is that supported groups must have incentives to
keep on paying the transfers. In principle, they could use the bargaining leverage
that foreign aid gives them to negotiate a deal with the opposition, but betray them
by promoting mass killings in the end of the period.
In case the supported group is the incumbent one:
1 1−δ
n
S−t− Ni
Ni+αNj
h
S−d− δ
1−δ(S−βNj)
io
≥S+ δ
1−δ(S−βNi)
The left-hand side of this inequality is the same that in the first restriction. The
right-hand side is the utility that the incumbent group gets by not paying the
trans-ferst, and then promoting total extermination of the rival group.
Notice that, if the opposition group is being supported and decides to deviate
and stop paying the transfers, punishment will be initiated, and in the next step, the
incumbent group will decide to fully exterminate them. Therefore, deviating would
yield him a payoff of 0, which is strictly lower than the payoff that it has by not
devi-ating.
Our first result is that the first restriction above is not possible to be attained by no
non-negative transfertin case the supported group is in opposition. In other words,
a necessary condition for the existence of a peaceful equilibrium in which the foreign
country supports the opposition group is for the foreign power to subsidize it. As it
will never be optimal for the foreign country to do so, we conclude that there is no
peaceful equilibria in which the supported group is in the opposition.
Proposition. 1. There is no peaceful equilibrium in which the foreign country
Doing backwards induction, we then analyse whether the group that has been
of-fered the deal has incentives to accept it or not. It accepts if its payoff of the following
subgame is greater or equal to the payoff induced by the punishment SPNE.
As shown in the appendix, by taking all those restrictions into consideration and
imposing non-negativity of the transferst(the foreign country will never be willing to
subsidize any of the groups), we have that the condition for an offer(α, t, j)to induce
a peaceful equilibrium is the following:
α≥ R+ (1−δ)β(Ni+Nj)−(1−δ)d
βδNj
Which is the same as the restriction found in Esteban et al. (2015) when we fix
α = 1. Notice that for every R there always exists anα great enough such that this
restriction is respected.
Finally, we have to analyse the foreign power’s choice on the offer(α, t, ℓ). As we
are restricting ourselves to peaceful equilibria, we can suppose that any SPNE of the
subgame following the offer of the foreign power to the opposition group features a
simultaneous decision by both the foreign country and the supported group to
can-cel the deal whenever possible. In this case, the foreign power would never have
strictly positive payoff by settingℓ=opposition group.
If there exists a pair(α∗
, t∗
)such that all the restrictions described so far are valid
andc(α∗
) ≤ t∗
, then it is possible to design a SPNE that prescribes that the foreign
country chooses (α, t,incumbent country), the incumbent country accepts, and a
peaceful equilibrium develops, and if anyone of the three actors deviate, they reverse
to the worst SPNE as a punishment. This leads us to Proposition 2:
Proposition. 2.Suppose there exists an(x, y)such thatx≥ R+(1−δ)β(Ni+Nj)−(1−δ)d βδNj >1
and c(α) ≤ y ≤ αNjδβNi−Ni(S−δβNi−(1−δ)d−δβNj)
αNj+Ni . Then, a SPNE with (α, t) = (x, y), in
which both countries engage in peace forever with no mass killings in the
equilib-rium path is enforceable in the model with foreign support, but not in the absence
Proof. See Appendix.
a
Welfare Analysis
A natural question that arises is whether foreign support raises the welfare of the
domestic country or not. To address this question, we compare the domestic welfare
in this model and the one obtained in Esteban et al. (2015)’s model.
First, whenever Esteban et al. (2015)’s model predicts that there is no loss in
wel-fare due to war (that is, peaceful equilibrium is possible), so it is in our model. It is
possible to design a strategy in which the foreign country offers(α, t, ℓ) = (0,1, incumbent),
incumbent country accepts if this specific offer is made and reject otherwise, the
op-position group always reject any offer, and continuation strategy follows according
to a peaceful equilibria.
In case it is not possible to enforce a peaceful equilibria with no foreign
assis-tance, one has to compare the loss os payoff due to war to the loss of payoffs due to
leaking of resources to the foreign country. Therefore, foreign assistance improves
domestic welfare if and only if:
t≤(1−δ)d+ 2δβ NiNj Ni+Nj
A sufficient condition for any peaceful equilibrium to be welfare-enhancing is for
the upper bound found in the last section to be larger than the right-hand side of the
inequality above. This is simplified to the following inequality:
(1−δ)d(Ni+Nj)(αNj+Ni)−δβNiNj[(α−3)Ni−(α+ 1)Nj]≥0
For this inequality not to be true, it is necessary forαto be very high,dto be
suffi-ciently low andNito be much larger thanNj. Intuitively, the transfers extract surplus
from the incumbent group, who by itself extracts surplus from the opposition group.
The higher theα, the higher is the bargaining power of the supported group, making
sur-implementation of the foreign support lowersi’s outside option of rebelling. As he is
going to have all its surpluss extracted, the higher is its population vis-`a-visj’s
popu-lation, the higher is the surplus thatj will extract with the aid of the foreign country,
and the higher it is willing to pay for transfers.
Below, there is a numeric example of a case in which there is a gain with foreign
assistance. May the parameters be as follows:
Example 1 Variable Value
β 1
δ 0.95
d 2
Ni 3
Nj 3
R 3.65
α 1.4684
t 0.1357
c(α) 18(exp(α−1)−1)
With these parameters,Rmust be lower or equal to 2.65 in order to exist a
peace-ful equibrium with no foreign aid, which is not the case. Being so, the national
sur-plus given by Esteban et al. (2015)’s model is equal to 134.
With these parameters, we needα≥1.36in order to exist a peaceful equilibrium,
which is clearly the case. The cost of providing α = 1.4684 is c(1.4684) = 0.0747,
which is lower than the transfers. Therefore, the foreign country is getting profits.
Total surplus of the domestic country is S−t
1−δ = 190.28, which is greater than the
5
Concluding Remarks
Esteban et al. (2015) found that countries that face low costs of civil war and
whose economies are highly dependent on natural resources and have low labor
pro-ductivity are more prone to facing ethnic cleansing events. Nevertheless, we
estab-lish that even on those cases, the presence of a self-interested foreign country that
supports partisanly one of the disputing groups may be able to drive the country to
a peaceful situation.
There are many examples of colonial powers preferring one ethnic group over the
others when colonizing a country. The most famous example was the Belgian
sup-port to the Tutsie ethnicity during the League of Nations/United Nations mandate in
Rwanda-Urundi(1922-1961). With independence of Rwanda in 1961, ethnic tensions
between Tutsies and Hutus rose to the point of facing civil wars and a genocide of the
tutsi minority. In Burundi, the Tutsies were responsible for the massacre of Hutus in
1972.
This case is not alone. There were civil wars in Sudan, Somalia, Djibouti, Eritrea,
Uganda, Kenya, Cˆote d’Ivoire, Liberia, Nigeria, Sierra Leone, Central African
Repub-lic, Republic of Congo, Democratic Republic of Congo, Chad, Zimbabwe,
Mozam-bique and Angola. One interesting exception are the former French colonies, as
noted by Collier et al. (2009). Our findings suggest that the military agreements
be-tween them and France play a large role in avoiding massacres to take place.
There are many possible extensions for this model. For example, one can
won-der how competition between different foreign powers affect internal disputes. One
good example would be the Chaco War, in which Royal Dutch Shell and Standard Oil
supported Paraguay and Bolivia, respectively, in a war between these two countries
to control the supposedly oil-rich Chaco region.
Another possible extension is to analyse how colonial powers design borders
After World War I, the Allies imposed a series of agreements to their defeated
ene-mies, and many of those included the creation of new countries and a redefinition
of borders5. In a similar fashion, Subsaharan African borders were defined by
Euro-pean countries, since those societies did not operate under the logic of nation-states.
5Some of those treaties were the Pykes-Sicot Agreement, the Treaty of Neuilly-sur-Seine, the Treaty
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A
Appendix
Suppose that the foreign country has offered {α, t} to country j and it has
ac-cepted. How does the subgame proceed? First, I will find the worst possible Nash
Equilibrium of the subgame to use it as a trigger strategy punishment in case one of
the players deviate in a peaceful equilibrium. I will assume thatt > c(α), such that it
is profitable for the foreign power to continue relations.
Claim 1: Just as in Esteban et al. (2015), because of the simultaneity during the war declaration stage, there is always an equilibrium in which both ethnic groups
decide to dispute power. Both groups are indifferent between deviating or not, since
dispute will be initiated anyway. Because of the surplus costd, the efficient
punish-ment phase of a grim trigger strategy must start with an internal dispute for power.
Claim 2: There always exists an equilibrium in which both the supported ethnic group and the foreign country decide to put their partnership to an end. Just as in
Claim 1, it follows from the simultaneity in the declaration of intentions. If one player
votes for the end of the military support, any action that the other player takes leads
to the same outcome, therefore making him indifferent.
Claim 3: In strategies following the characteristics featuring in Claims 1 and 2, war forever cannot be sustained as an SPNE.
Suppose both groups, when winning a dispute, decide to do no mass killings in
any following period. Therefore,ℓ’s payoff would be:
S−d+ δ 1−δ
Nℓ
Nℓ+N−ℓ
(S−d)
Notice that it does not matter whether the winning group is supported or not
because, for Claim 2, the supported group will not pay transfers t and the foreign
power will withdraw its support in the beggining of next period. Ifℓdecides for total
S−d+ δ
1−δ(S−βN−ℓ)
which is strictly larger than the previous one. Therefore, this cannot be a
subgame-perfect Nash equilibrium
Claim 4:There exists an SPNE strategy in which both ethnic groups always choose to confront each other, the winner decides to do full extermination of its rivals, the
supported group decides to pay transferst = 0and the foreign power withdraws its
support in the first opportunity.
The first affirmation comes from Claim 1. To prove the second point, suppose
that the affirmation is true. Notice that the payoff group ℓgets from deviating and
eliminatingM ∈[0, N−ℓ)is given by:
S−d+ Nℓ
Nℓ+N−ℓ−M
δhS−βM−d+ δ
1−δ(S−βN−ℓ)
i
,
which is always lower than the payoff of doing full extermination.
This brings us to Lemma 1:
Lemma. 1.The strategy profile described in Claim 4, consisting of both ethnic groups
always disputing for power and promoting mass killings after winning it, whereas the
supported group and the foreing power put an end to the military foreign support in
the first possible opportunity, is the worst SPNE of the subgame starting after the
refusal or acceptance of the foreign power proposal in periodτ = 0.
To suspend military aid is a punishment for the supported group (anything that
it could enforce in equilibrium without support, he still can with support) and for
the foreign country, in caset ≥ c(α), since ceases to receive profits. In principle, it
cannot be seen as a punishment for the unsupported country. Nevertheless, as we
are going to focus on peaceful equilibria, in any deviation by the opposition group
that stars a punishment strategy with features from both Claims 1 and 2, civil war is
Therefore, dropping or sustaining the support will make no difference in its payoff.
Having the most efficient punishment, we can characterize the best possible
equi-libria. First, I will follow Esteban et al. (2015) and define fairness level.
Definition 2. If in the begining of the period, the incumbent groupℓoffers a total of
Yτ to its foe−ℓ, than, in that period, the fairness level will beλτ such that:
Yτ =λτ N−ℓ Nℓ+N−ℓ
S
In SPNE in which there is no dispute nor mass killings, the incumbent country
will define the fairness levelλin order to make the other group indifferent between
accepting or rejecting the offer. If it accepts the offer, the groupN−ℓreceives a payoff
1 1−δ
λ N−ℓ Nℓ+N−ℓ
S−t
wheret = 0if it is not supported. If it rejects and is not supported by the foreign
power, it gets:
N−ℓ
αNℓ+N−ℓ
S−d+ δ
1−δ(S−βNℓ)
If it rejects and is supported by the foreign power, it gets:
αN−ℓ
Nℓ+αN−ℓ
S−d+ δ
1−δ(S−βNℓ)
Suppose thatj is the supported group. Therefore, to make it indifferent, the
in-cumbent ethnic affiliation must set
λi =
Ni+Nj
Ni+αNj
S−(1−δ)d−δβNj
S
if its foe receives no support and
λj =
Ni+Nj
Nj
t S +
α(Ni+Nj)
Ni+αNj
S−(1−δ)d−δβNj
S
1−λj
Nj
Nj +Ni
S
1−δ =
NiS+αNj (1−δ)d+δβNj
(Ni+αNj)(1−δ)
− t
1−δ
And if it isj, its discounted payoff is:
1−λi
Ni
Nj+Ni
S
1−δ − t
1−δ =
N i (1−δ)d+δβNj
+αNjS
(Ni+αNj)(1−δ)
− t
1−δ
The offer that the foreign country makes must respect two restrictions. First, the
ethnic group must accept the offer. Second, it must be the case that it has incentives
to keep paying the transfers proposed.
First, suppose that the foreign power makes the offer(α, t)to the group that is not
in power. By using the strategy described in Lemma 1 as a punishment for deviations,
we have thati’s payoff of deviating and not accepting the offer is Ni
Ni+αNj S−d+
δ
1−δ(S−
βNj)
. Therefore, the foreign country only has to comparei’s payoff of accepting the
deal withi’s payoff induced by the strategy in Lemma 1. The restriction forito accept
the deal(α, t)is, then:
NiS+αNj (1−δ)d+δβNj
(Ni+αNj)(1−δ)
− t
1−δ ≥
Ni
Ni+αNj
S−d+ δ
1−δ(S−βNj)
which yields the following equation:
t≤(1−δ)d+δβNj
The restriction that makesistill prefer a peaceful payoff to do mass killings is6:
NiS+αNj (1−δ)d+δβNj
(Ni+αNj)(1−δ)
− t
1−δ ≥S+ δ
1−δ(S−βNj)
which simplifies to:
t ≤ N i(δβNj) +αNj(−S+ (1−δ)d+ 2δβNj)
Ni+αNj
6The incumbent country always prefers to deviate when choosing how much of the rival
Notice that the right-hand side of this inequality is lower than 0 whenα = 1, and
it is decreasing inα7. As the foreign country would never be willing to offer a contract
with a negativet, we conclude that it never offers an contract to the group that does
not hold power. This gives us Proposition 1:
Proposition. 1. There is no peaceful equilibrium in which the foreign country
sup-ports the ethnic affiliation that is not in power.
Suppose now that the foreign power makes the offer(α, t)to the incumbent group.
If the incumbent rejects the deal, the equilibrium that follows is as described in
Lemma 1. In that case, the first restricition is:
N i (1−δ)d+δβNj
+αNjS
(Ni+αNj)(1−δ)
− t
1−δ ≥ Nj
Ni +Nj
S−d+ δ
1−δ(S−βNi)
Or, equivalently:
t≤ αNj SNj +Ni(1−δ)d+δβN
2
i
+Ni
(Ni+Nj)(1−δ)d+δβ(Ni2+NiNj +Nj2)−NiS
(Ni+Nj)(Ni+αNj)
The second restriction is as depicted below:
N i (1−δ)d+δβNj
+αNjS
(Ni+αNj)(1−δ)
− t
1−δ ≥S− δ
1−δ(S−βNi)
Which can be restated as:
t≤
αNjδβNi −Ni
S−δβNi −(1−δ)d−δβNj
αNj+Ni
Which is greater or equal to zero if and only if:
α ≥ R+ (1−δ)β(Ni+Nj)−(1−δ)d
βδNj
(Feasibility Restriction)
Ifα = 1, the feasibility restriction above is the same as the one found in Esteban
restriction is lower than the right-hand site of the first restriction. In this case, there
is no loss in ignoring the decision to accept or not, and only focus on the incentives
to keep paying the transfers.
In Esteban et al. (2015), if R+(1−δ)β(Ni+Nj)−(1−δ)d
βδNj >1, apeacefulequilibrium was not
possible. Now, as long as there exists oneα≥ R+(1−δ)β(Ni+Nj)−(1−δ)d
βδNj such that the cost
c(α)incurred by the foreign power is lower or equal to
αNjδβNi−Ni
S−δβNi−(1−δ)d−δβNj
αNj+Ni ,
it is. In other words, by inserting the foreign power as a principal, influencing on the
probabilities of victory inside the country, we may be able to induce peace in
situa-tions where it was not possible with no foreign influence.
Going back one step, it is always possible to enforce any(α, t,incumbent group)
such thatα andt attend the restriction above and t ≥ c(α). Imposing that, in any
subgame following the acceptance by the incumbent group in which the offer was
different from this specific(α, t,incumbent group), players coordinate into the worst
SPNE, otherwise they coordinate into the peaceful equilibria. These are, by
construc-tion, SPNE of that subgame.
In such a strategy, the foreign power gets a non-negative payoff of offering(α, t,incumbent
group)and a non-positive of choosing any other option. Therefore, it is optimal for
him to choose(α, t,incumbent group). This leads us to Proposition 2.
Proposition. 2.Suppose there exists an(x, y)such thatx≥ R+(1−δ)β(Ni+Nj)−(1−δ)d βδNj >1
and c(α) ≤ y ≤ αNjδβNi−Ni(S−δβNi−(1−δ)d−δβNj)
αNj+Ni . Then, a SPNE with (α, t) = (x, y), in
which both countries engage in peace forever with no mass killings in the
equilib-rium path is enforceable in the model with foreign support, but not in the absence
of it.
a
Welfare Analysis
We analyse welfare by establishing weight 1 to the foreign country and weight0to
in Esteban et al. (2015) are different, and thus the comparison between them is not
perfect. By setting the weight of the foreign country to 0, only the domestic country
is being taken into account, and comparison is more direct.
The global welfare in a peaceful equilibrium with foreing offer given by(α, t, j)is
given by:
1
1−δ[S−t]
Whereas in the case with no foreign support8, the payoff of the best SPNE is given
by the expression below:
S
1−δ ifR≤βNj −(1−δ) β(Ni+Nj)−d
,
S−d+ Ni
Ni+Nj
δ
1−δ(S−βNj) + Nj
Ni+Nj
δ
1−δ(S−βNi) ifR > βNj−(1−δ) β(Ni+Nj)−d
IfR ≤βNj−(1−δ) β(Ni+Nj)−d
, it is always possible to have a peaceful
equi-libria in which the foreign country offers(α, t, ℓ)= (1,0, incumbent), the incumbent
group accepts if it is offeredα = 1and t = 0and rejects otherwise, the opposition
group always reject, and if the offered group rejects, then they coordinate into the
worst SPNE. In this case, the global surplus in our model and in Esteban et al. (2015)’s
is going to be exactly the same.
IfR > βNj−(1−δ) β(Ni+Nj)−d
, the picture is a little less clear. Global welfare of
the model with foreign support is greater or equal to the one in the one in the model
without it if the following inequality holds:
S−t≥S−(1−δ)d−2δβ NiNj Ni+Nj
which can be restated as (supposing there is foreign aid and the foreign country
gets a strictly positive payoff ):
t≤(1−δ)d+δ2β NiNj Ni+Nj
We will now look for some sufficient conditions. Ifc(α)≤(1−δ)d+δ2β NiNj
Ni+Nj and
c(α) ≤ αNjδβNi−Ni(S−δβNi−(1−δ)d−δβNj)
αNj+Ni , then it is always possible to find a t such that
there is a peaceful equilibrium andc(α)< t <(1−δ)d+δ2β NiNj
Ni+Nj.
Nevertheless, it still can be the case in which:
(1−δ)d+δ2β NiNj Ni+Nj
< c(α)< αNjδβNi−Ni S−δβNi−(1−δ)d−δβNj
αNj+Ni
for alll α that respects the conditions in Proposition 1. In that case there could
be a loss in welfare. A necessary condition for this to be possible is for (1−δ)d+
δ2β NiNj
Ni+Nj <
αNjδβNi−Ni S−δβNi−(1−δ)d−δβNj
αNj+Ni . Putting this together with the restriction
onR < βNj−(1−δ) β(Ni+Nj)−d
and simplifying the algebra, we get the following
necessary restriciton:
(1−δ)d(Ni+Nj)(αNj +Ni)−δβNiNj
h
(α−3)Ni−(α+ 1)Nj
i
≤0
For this to be true, it is necessary thatαis high enough,dis low enough and that
