1. Introduction
In this paper we set out an elementary game-theoretic model of conflict between groups based
on individual behavior. We focus on the role of heterogeneity both between and within groups
in explaining conflict. Individuals differ not only in the group they belong to — their “ethnic-
ity” — but also in their wealth and in the radicalism of their commitment to the group’s cause.
The within group heterogeneity in wealths and radicalism is the main novelty of this paper. Be-
sides examining the more standard issue of whether higher heterogeneity across groups leads
to higher conflict, we also study the role of within-group homogeneity. As is now well-known,
both these features have been highlighted in recent literature on the conceptualization and mea-
surement of polarization.1
The model is extremely simple, and is to be regarded more than anything else as a tool to clas-
sify different factors in conflictual situations. But even in this stripped-down form the model
yields some insights, arguing — for instance — that economic inequality within ethnic groups
rather than across them is likely to be a potent force in determining the extent of ethnic vio-
lence. This sort of model may therefore be useful, because in spite of the continued attention
to the issue of ethnic/religious conflict analysts appear quite far from a minimal agreement on
its basic driving forces. In his comprehensive survey Horowitz (1998)2 lists up to ten distinct
explanations for social conflict, some substitutes for each other, some complementary. To each
such family of explanations he produces countering facts. This variety of possible causal factors,
while rich, can be at the same time confusing and not easily amenable to empirical falsification.
A first major concern in the analysis of religious/ethnic conflict is to account for the obvi-
ous passion and rage overwelmingly present on either side of the ethnic divide. Writers such
as Horowitz (1985, 1998) and Brewer (1979, 1991 and 1997) have argued that the success of the
group has value per se, quite independently of the material benefits that the group members
could derive from a victory over the opponent. Horowitz (1998) stresses the role of passion
along with sheer material interest in explaining individual behavior in conflict. In the exercise
that follows, we will let individuals be motivated by group success — conceived of here as the
payoffs from an “ethnic public good” — and we permit these payoffs to vary across individ-
uals as well the direct material components of their well-being. In this sense, we marry the
rational choice tradition with a broadening of the notion of individual motivations, including
non-material, group-defined rewards.
A second goal of this paper is to emphasize the different roles played by economic factors.
Typically, economic wealth plays a double role. The first role is one we do not particularly
emphasize, though we allow for it: wealth determines the stakes in case a victory over the
opponent comes with (possibly partial) expropriation of the opponent’s resources. From this
angle, we should expect that the larger are wealth differences across groups the more likely it is
that conflict will break out. This is the view held by Wintrobe (1995) who views inter-group envy
as a major cause of conflict. In the same vein, Stewart (2002) identifies “horizontal inequality”
across groups — the existence or the perception of an unjustly widening economic gap between
them — as a major source of ethnic conflict.
Two considerations militate against this point of view. First, whether or not inter-group
inequality is conflictual depends crucially on whether the economically weaker group or the
stronger is the instigator of conflict.3 While we do not pursue this particular thread here, we
follow a complementary line of reasoning by emphasizing a second role played by wealth: that
1See Esteban and Ray (1994) and Duclos, Esteban and Ray (2004) for the notion and measure of polarization and
Esteban and Ray (1999) for the role of polarization among groups in conflict.
2See also his classic, Horowitz (1985).
3Pande and Ray (2003) make this point.