Cooperation in Violent Conict: a Model of Common Fate David Hugh-Jones Max Planck Institut fur Ökonomik, Jena

Abstract The stylized facts of intergroup conflict include the following: most groups live at peace; violence can erupt suddenly, and has an important symbolic dimension; group identity is easily created even by outsiders, especially by threats. No current theory satisfactorily explains all of these features. I suggest a simple explanation for all these: the dynamics of cooperation in conflicts. When these are taken into account, participation in conflict may be rational for materially self-interested individuals, even without incentives such as punishment from one’s own side. Modelling the collective action problem formally leads to different predictions from a model with unified groups. The conclusion discusses possible applications to the formal theory and social psychology of group conflict.

F IRST DRAFT

1 Introduction The theory of public goods tells us that when an action benefits others as well as the actor, that action is likely to be undersupplied. Wars and other episodes of violent conflict are puzzling for rational choice theories of human behaviour, because they involve humans risking injury or death in a cooperative endeavour. This is particularly true of conflicts where the sides are not organized armies but informal groups - for example, riots and some civil wars. Armies can credibly threaten to shoot deserters or cowards. An informal group will find it harder, since violence within the group will weaken its ability to fight the enemy. Rational choice modellers have taken two paths in response to this difficulty. Many theories of social conflict, whether ethnic or class-based, simply bypass it by treating groups as the relevant actors (Acemoglu and Robinson (2006) and Boix (2003) are two important recent examples). Simplifications like this are legitimate and essential for many kinds of political economy. But without a solid foundation for the underlying 1

1 Introduction

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C D Tab. 1:

C 4,4 3,1

D 1,3 2,2

The Stag Hunt.

individual cooperation, these arguments are like the mathematician in the New Yorker cartoon, whose colleague tells him “I think you should be more explicit here in step two”. Step two consists of the words “and then a miracle occurs.”1 The other approach is to tackle the difficulty head-on and try, like the present paper, to show that cooperation in conflict can indeed be individually rational. The simplest method is to change actors’ utility functions. For example, participants in conflict might be “parochial altruists” who care about the welfare of others in their group. This is not vacuous: interesting and testable predictions can be derived from the resulting models. But it does involve making a special assumption which is not generally made in other fields. Two other often-used explanations are punishment and the Stag Hunt. “Punishment” invokes the theory of repeated interactions, where numerous Folk Theorems demonstrate that cooperative behaviour may be sustained in equilibrium by the threat of punishment from other players. In the Stag Hunt, shown in Table ??, there are two Nash equilibria.2 Players are willing to cooperate (C) so long as they expect others to do so as well. If they expect others to defect (D), they defect themselves. If the payoffs from cooperation in conflict had this structure then we might reasonably expect to see cooperation. Taking punishment first, there is clear evidence that some participants in warfare are compelled to fight (e.g. Mueller 2000). Nevertheless, it seems unlikely that this can be the whole story. Conflict is unpredictable. The identity of one’s compatriots may change rapidly, and they may not be people with whom one has established bonds of long-term reciprocity. Forces without a formal command structure face a further problem: “punishment” of one group by another on the same side may lead to retaliation and internecine feuding, a point first made by Locke and confirmed in laboratory experiments. The Stag Hunt is, on the face of it, implausible. It requires that when others cooperate, one would prefer to do so also, because one’s share in the gains outweighs the benefits of defection. (In the original story, if all cooperate they catch a stag, which provides more meat per individual than the rabbit a defector catches.) Defence, however, is usually thought to be a classic public good: the gain from cooperation is that the enemy is defeated, and this benefit is shared by cooperators and non-cooperators alike. As a result of these weaknesses, many researchers have dismissed rational choice explanations of conflict as unfounded. For example, Petersen (2002) writes: “... any act by an individual against a large group,... is inherently irrational in the Olsonian sense.“ 1

This analogy comes from Hardin (1995). This use of the Stag Hunt is different from that famously introduced by Jervis (1978). There the two players are on different sides of a potential conflict, and cooperation (C) means peaceful behaviour. Here, players are all on the same side and cooperation means fighting together. 2

1 Introduction

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Kaufman (2001): “pursuit of individual self-interest does not explain torture, murder or risking one’s own life in battle.” Similar comments can be found in work by social psychologists and political scientists (e.g. Halevy, Bornstein and Sagiv, 2008; Dawes, 1980). The main aim of this paper is to show that large-scale cooperation in violent conflict can be explained as an outcome of rational decisions by materially self-interested actors. To do so, I propose a straightforward and intuitive rational choice theory of such cooperation. I do not claim that the theory explains all the data. But it does apply quite widely. Also, my explanation uses factors specific to violent conflict, which existing theories do not. RCT explains people’s actions based on their predictable interests and on predictable, often measurable features of the situations they find themselves in. So, even if interests and constraints do not explain all or much of the observed variation in behaviour, it may be more useful to focus on them than on emotions, myths and rhetoric, which are harder to measure or predict. A second point of the paper is that modelling individual actors within a group can change our expectations, as suggested by Blattman and Miguel (2008). I show that qualitatively different predictions emerge when we take into account the collective action problem within one side in a conflict. Finally, the perspective advanced here accounts for a number of stylized facts which emerge from the large and diverse literature on ethnicity and inter-group conflict. Therefore, it proposes a single pattern underlying many kinds of data, as a good scientific theory should. The explanation put forward here is not new. Historically it is commonly advanced as a reason for action. My favourite example is Martin Niemoller’s famous quotation: When the Nazis came for the communists, I remained silent; I was not a communist. When they locked up the social democrats, I remained silent; I was not a social democrat. When they came for the trade unionists, I did not speak out; I was not a trade unionist. When they came for the Jews, I remained silent; I was not a Jew. When they came for me, there was no one left to speak out. This is usually thought of as an ethical precept. In fact it contains a straightforward appeal to self-interest. The idea of the quotation is that dynamics matter. An episode of cooperation that appears irrational or selfless in the short term may be rational when we examine the long-term consequences of failure to cooperate. Individuals cooperate in conflict, on this view, for the same reason that Britain has traditionally intervened in continental wars: not from altruism, but from fear that it might be targeted if any one power became dominant. Specifically, the dynamics of the situation transform a shortterm Prisoner’s Dilemma into a Stag Hunt. Although it is common sense, this argument has not been explicitly made in the literature on ethnic conflict and civil war, so that

1 Introduction

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rational choice explanations have been mistakenly undervalued. And formalizing the argument leads to insights that are not ex ante obvious. In the remainder of this section, I present some stylized facts about conflict between groups. In each case I show how they relate to this basic idea. Section 2 discusses existing models of cooperation in conflict, from within and beyond the rational choice approach. Section 3 presents the underlying model and shows the conditions for cooperation. Section 4 simplifies the model to show how within-group conflict of interest makes a difference. The conclusion discusses further theoretical work, and the potential for developing a social psychology of group membership on rational-choice foundations.

1.1 Stylized facts about groups in conict “Groups” are universal features of human existence, but the concept has no single clear interpretation, and different disciplines see it from different perspectives. As a result, the literature is large and diffuse. Some core ideas, however, recur in different intellectual frameworks. I draw in particular on the literature on ethnic groups, a politically important category, broadly defined to include any group whose membership is transmitted by descent; also on social psychology and narrative accounts of civil war. Ethnic groups usually live in peace

Fearon and Laitin (1996) make this point most forcefully. Although conflict between ethnic (and other) groups is endemic, it is usually resolved peacefully by formal or informal channels, not by violence. Most ethnic groups live in peace most of the time. And over history, different ethnic groups have persisted in the same locality. Why should this be so? Part of the answer is that the state enforces peace. But states are not always impartial referees in ethnic conflict, and when they are, this too needs explanation. One fundamental factor that limits the appeal of conflict is the asymmetrical motivation between defenders and attackers. The potential payoff for attacking members of another group is booty, the physical or human assets which can be stripped from the losers. The payoff for defending one’s own group is survival. Booty is a powerful motivator, but it is also rival: what I have, my fellow group members lose. It is a commonplace of history that winners quarrel over the spoils. Survival, on the other hand, is often achievable only by all or none of a group, since survivors are vulnerable to further attacks. In terms of motivation, then, defenders have the upper hand. For this reason, in general, anarchy is not a war of all against all,3 and the state prefers to manage different ethnicities rather than eliminate them. 3 Except perhaps in Hobbes’ original sense: “not in battle only, or the act of fighting, but in a tract of time, wherein the will to contend by battle is sufficiently known” (1651).

1 Introduction

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Violence can be sudden and unexpected

In Prijedor there were no conflicts between nationalities. We didn’t make the distinctions.... When we were children we went to the Orthodox church or the mosque together... I don’t understand. Bosnian Muslim, quote reproduced in Oberschall (2000) A recurrent theme in civil war is the peaceful village whose inhabitants suddenly turn against their neighbours. Two kinds of models have been suggested to explain on this process. One refers to multiple equilibria in the level of public “ethnic” behaviour , since one person’s public display increases the pressure on others to follow suit Kuran (1998). This is similar to a “punishment” argument (see above and Section 2). Another is the security dilemma (Jervis, 1978; Posen, 1993; Lake and Rothchild, 1996). On this account, different groups are playing a Stag Hunt (see again Table 1 on page 2) with each other: they would prefer to live at peace, so long as the other group does so too. The suddenness of violence is a reflection of this game’s multiple equilibria. Best responses are mutually dependent, and so spirals of mistrust are mutually reinforcing. This explanation is powerful and has been found convincing even by theorists who do not in general turn to rational choice explanations(Petersen, 2002; Kaufman, 2001). To complement it, an explanation of why violence spreads is needed. (Civil war is more than a series of small-scale local interactions.) When attack and defence are difficult to distinguish, a spiral of mistrust can increase levels of cooperation within groups. Increasing mobilization of the other side makes it more likely that an attack will not be limited in time or scope, but will aim at one’s own entire group. This in turn makes cooperation to defend one’s co-ethnics more attractive, since failure to do so will increase one’s own future vulnerability. ... with a symbolic dimension

At its worst, intergroup conflict is notoriously cruel. The forms of violence inflicted on the defeated often seems to aim at humiliation (Horowitz, 2001; Petersen, 2002). It is natural to turn away from rationalist theories and towards explanations based on emotions. Here a concern with the within-group collective action problem really pays off, by reconciling these perspectives. The symbolic and ritualized aspects of violence can be thought of as costly signalling. Exposing the other group’s powerlessness, in the most visible way, sends a public signal of the group’s weakness, lowering its members’ incentives to fight together and thus damaging its cohesion. This argument depends on multiple equilibria in the within-group collective action problem, as in the Stag Hunt. Group identities can be created easily

The best evidence for this comes from the “minimal group paradigm” in social psychology (Tajfel et al., 1971; Tajfel, 1982). Seeking the weakest possible experimental manipulation that would induce people to discriminate between those in their own

1 Introduction

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group and those in another, Tajfel and his colleagues found it was very weak indeed. If subjects were allocated randomly, or on the basis of irrelevant preferences, into groups, without common knowledge of group membership and without self-interest in group outcomes, they nevertheless discriminated in their allocation of money between ingroup and outgroup members.4 The same lessons also come out of political science narrative work, where it is repeatedly claimed that media or politicians’ rhetoric can manipulate people’s sense of group identity (Gourevitch, 1999; Kaufman, 2001; Oberschall, 2001; Bauerlein, 2001; Fearon and Laitin, 2003). The puzzle is why individuals are susceptible to these appeals. Niemoller’s quotation suggests why. The boundaries of reasonable cooperation are not given by pre-defined identities (Jews, Communists, Trades Unionists), but by the other side’s intentions. A believable public statement that all the Hutus intend to massacre all the Tutsis is a great way to bring all the Tutsis together, which in turn will bring the Hutus together. Thus, elite rhetoric can affect the boundaries of cooperation in conflict. ... especially by external threats

On the account advanced here, individuals’ group commitment comes from their sense of threat, and indeed the relationship has long been observed. Sumner (1906) wrote “The relationship of comradeship and peace in the we-group and that of hostility and war towards other-groups are correlative to each other. The exigencies of war with outsiders are what makes peace inside” (quoted in Tajfel 1982), while Simmel’s rule states: “the internal cohesion of a group is contingent on the strength of external pressure“ (Simmel, 1955). The theory is confirmed by experimental work in social psychology (Stephan et al., 2005) and is the basis of Realistic Group Conflict theory, discussed further below. Other work emphasizes that threats to the group can be both realistic and symbolic (Kinder and Sears, 1981; Stephan and Stephan, 2000), consistently with this paper’s theory: symbolic issues, like symbolic violence, can signal a group’s strength or vulnerability. Lab identities matter more than real ones

A final, surprising pattern in experimental work is that “real” group membership ethnic or national - often seems to matter less than the “minimal” groups created by experimental manipulation in the lab. (See Habyarimana et al., 2007; Whitt and Wilson, 2007; Fershtman and Gneezy, 2001; Bouckaert and Dhaene, 2004 for real groups; compare Goette and Huffman, 2006; Chen and Li, 2006; Hargreaves-Heap and Varoufakis, 2002; HEAP and ZIZZO, N.d.; McLeish and Oxoby, 2007 for lab groups. In Bernhard, Fischbacher and Fehr, 2006, New Guinea tribesmen discriminate strongly against ethnic outgroups; contact between these groups is perhaps rarer than in the 4 These results have been broadly confirmed in economics experiments without deception and with realmoney payoffs (Chen and Li, 2006).

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other examples.) But if group loyalties are created by threats, then real groups which live together will have developed mechanisms to avoid threatening each other and precipitating conflict (Fearon and Laitin, 1996). Lab groups, on the other hand, are new groups. They are not inherently weaker than old groups, since group membership is determined by how others see you rather than an abiding feature of your personality; they lack mechanisms for avoiding threats; and their newness can cause uncertainty about relative strengths, leading to conflict.

2 Existing Theories of Cooperation in Conict 2.1 Rational choice theories It will help to formalize the basic problem. Suppose that a group of N individuals faces an enemy. Each individual must choose to cooperate (C), paying a cost α, or costlessly defect (D), in the resulting conflict. The probability of the individuals winning is p(x) where x is the number playing C; we assume p(0) = 0. If they win, the enemy is defeated, and all individuals receive a payoff of one; if they lose, one individual is chosen at random and receives a payoff of 0. (If the individual who will suffer is known beforehand, nobody else has any incentive to cooperate. Equivalently we could assume that everybody suffers a deterministic loss of 1/N.) Observe that cooperation at x is efficient (maximizes the summed utility of the individuals) if and only if p(x + 1) − p(x) ≥ α

(1)

, since the loss to the group from defeat is a sure 1. If this condition does not hold at a given x, there is no collective action problem: defection is efficient. Individuals cooperate if −α + p(x + 1) + (1 − p(x + 1))(1 −

1 1 ) ≥ p(x) + (1 − p(x))(1 − ) N N

(2)

assuming they believe that x others will cooperate. Equivalently: p(x + 1) − p(x) ≥α N

(3)

When N is large, for this to hold requires α to be small so that cooperation costs little. For p(x + 1) − p(x) ≤ 1 in any case. Thus, costly actions such as taking part in violence seem to be ruled out. One way out is to assume that the situation is repeated, and that individuals can condition their behaviour on their own and others’ previous play. If so, well-known Folk Theorems show that cooperation can be sustained if individuals are patient enough. Equilibrium takes something like the following form: everybody cooperates so long as nobody else has defected, but if anyone defects, everybody defects forever thereafter. Defection after defection is individually rational if (3) is violated; initial cooperation

2 Existing Theories of Cooperation in Conict

8

is rational because one’s own defection will cause everybody to defect in subsequent periods, thus reducing the number of cooperators to 0 and giving a sure loss of 1/N.5 In effect, one individual’s defection is punished by everyone else’s defecting. Thus on the equilibrium path nobody ever defects. The idea of punishment chimes with observations of within-group sanctions for nonparticipants in conflict (Mueller, 2000; Beber and Blattman, N.d.), and it has been invoked by theorists as an explanation of group violence (Hardin, 1995; Fearon and Laitin, 2003). However, two points are relevant. First, punishment here is “in equilibrium”: the punishment here involves everyone behaving selfishly. The kinds of punishment seen in warfare tend to involve violence specifically against the defectors. There is thus a second-order collective action problem. Second, full cooperation in repeated games is an artefact of the assumption of perfect monitoring - all players always correctly observe all others’ actions. When actions can be hidden or observed with error, individuals have incentives to defect but conceal that fact; and equilibria involve intermittent periods of universal defection, which would be problematic during warfare. Concretely, decentralized punishment leads to feuds, as Locke ([1690] 1988) observed and as modern experimental work confirms (Ostrom, Walker and Gardner, 1992); again, the resulting internecine conflict could be exploited by an enemy. Thus, although punishment may explain some participation in violence, it seems insufficient to explain all of it.6 A second explanation is that some or all players have Stag Hunt style payoffs: they prefer to cooperate if everybody else cooperates. (Hardin combines this and the punishment explanation: “extremists” have larger gains than others from cooperation, and they will cooperate and will punish non-cooperators.) An interesting twist is the claim that groups tailor the form of cooperation to create Stag Hunt situations where the outcome depends on everybody taking part (Chong, 1991; Popkin, 1979). We can always make this assumption: undoubtedly there are satisfactions from fighting together. But if we do so, we are solving our problem by assumption, and making cooperation depend on factors that are intrinsically hard to measure or predict. On the other hand, in the framework above, where the only gain from cooperation is the instrumental increase in the probability of defeating the enemy, Stag Hunt payoffs do not fit. Even if winning or losing depends only on my action (p(x + 1) − p(x) = 1), cooperation will still require α < 1/N which becomes small as N becomes large.

2.2 Other models Social psychologists have developed several explanations for the behaviour observed in minimal group experiments. These explanations often include elements of rational5 Formally, cooperation is rational iff 1 (p(N) + (1 − p(N)) 1 − α) N 1−δ 1 1 δ N ) + 1−δ (1 − N ), where δ is the discount rate. 6 A third point comes from the phrase if individuals are patient enough.

≥ p(N − 1) + (1 − p(N − 1)(1 −

Individuals who value the present highly are likely to defect. The battlefield, by definition, is a situation where immediate payoffs are extremely high - survival or death, so we would expect these equilibria to be unsustainable in truly dangerous situations. I have not emphasized this issue, since it applies equally to the explanation advanced here. In fact, the “discount rate” has some interesting interpretations, discussed below.

2 Existing Theories of Cooperation in Conict

9

ity. They may also be linked to rational choice theories by evolutionary arguments: we behave as we do because that has proved optimal for our survival in the past. Nevertheless, the focus is more on the arational features of human behaviour.7 The dominant theory of ingroup prejudice is Social Identity Theory(Tajfel et al., 1971; Tajfel, 1982). This explains behaviour favouring the ingroup as self-esteem management. Part of our sense of identity comes from the groups we belong to. When threats to that identity – such as derogation of our group by outsiders – appear, we may respond by trying to leave the group, or by bolstering our sense of the group’s worth, perhaps by derogating, or actively discriminating against, those in outgroups. Social Identity theory has a solid track record of predicting laboratory behaviour. However, it has limitations. The logic works best as a theory of “ingroup love” rather than “outgroup hate” (Brewer, 1999), and indeed it is hard to create discrimination in the lab when people are allocating negative payoffs (Mummendey et al., 1992). Fundamentally, finding the roots of our attachment to groups in self-esteem seems to put the cart before the horse. Groups are fundamental to our identity because of the protections and dangers we derive from belonging to them, not the other way around. More venerable still is Realistic Conflict Theory (Sherif et al., 1961; Campbell, 1965), which proposes that intergroup hostility occurs when groups have conflicting goals, and can be reduced when groups have superordinate goals requiring them to work together. Threats to group safety are one particular kind of conflict – others may be threats to economic interests or social status. Realistic Conflict Theory thus appears robustly materialist. However, it contains no explanation of why individuals should act in the interests of the group; indeed Campbell’s original paper describes ethnocentrism as an altruistic motive and invokes group selection to explain it. In general, we would expect collective action problems to bite deeply. In the specific case of violent conflict, as this paper shows, they need not do so. Reciprocity Theory (Yamagishi and Kiyonari, 2000) takes issue with Social Identity Theory on the interpretation of minimal group experiments. It claims that ingroup favouritism is founded on an evolved heuristic to expect reciprocity from fellow group members: ingroup bias is an instinctive application of the theory of repeated games. Like SIT, however, reciprocity theory cannot really explain behaviour towards outgroups. Social Dominance Theory (Sidanius and Pratto, 1999), on the other hand, tries to explain individuals’ levels of outgroup bias. The theoretical argument is that all societies are stratified into higher and lower groups, and that individuals vary in their desire for this stratification. In particular, robust differences between the genders have been found in this regard. However, the correlation of social dominance orientation – a questionnaire-based measure of support for inequality and hierarchy – with in-group favouritism, is unsurprising, and compatible with many possible explanations. The ideas closest to this paper come from biology. Hamilton (1971) explained group living and herding by the “dilution effect”: an individual in a large group is more likely to survive attack by a predator. Since individuals gain from the size of their group, they 7

For a fuller review of these models, see Hewstone, Rubin and Willis (2002).

3 The Model

10

have an interest in acting to preserve it and this may stabilize altruistic defence against predators (Garay, 2008; see also Eshel, Samuelson and Shaked, 1998).

3 The Model We develop the framework of the previous section. At the start of play there are N group members. They share a common discount factor δ . Each round, each player that remains alive receives some utility. We normalize payoffs so that the value of staying alive for a single round is 1 − δ ; then the value of staying alive for ever is 1−δ 1−δ = 1. At first, we will allow δ to go to 1. The idea is that when the value of surviving a single extra round is low compared to the value of a final victory – perhaps because conflict is fast-moving – the temporary gains from defection become low. Group members face a common enemy. For the moment, we assume the enemy is nonstrategic, and simply attacks each round until he loses. Alive group members may pay a cost α to Cooperate (C) against the enemy. Or they may Defect (D) and pay no cost. The probability of the enemy losing is p(x) where x is the sum of players playing C. We assume p(0) = 0 and p is strictly increasing. If the enemy wins, one random remaining player leaves the game and gets 0 forever. After the enemy loses, all remaining players can Defect forever and thus get a total utility of 1. This is the highest possible value in the game, starting from any round. When there are m players remaining, write the value for a group member as Vm . Let VmD be the value to a player when the group has m remaining members and assuming that all members defect for all remaining periods. Thus m−1

VmD = (1 − δ )

∑

s=0

m−s s δ m

(4)

where (m − s)/m is the probability that the group member remains alive after s further rounds. Since other players’ Defection decreases one’s probability of survival, and since Vm is a player’s value from his optimal strategy and “defect forever” is a possible strategy, VmD 6 Vm for all m. (5) Also, it is immediate from the definition that VmD → 0 as δ → 1.

(6)

That is, when players are sufficiently patient, the value of survival for a fixed finite number of periods is negligible compared to the value of survival “forever” after victory. We write p0 (y) = p(y) − p(y − 1). Suppose that a single round of conflict decides whether all players live or die. Then, when x other players cooperate, a player cooperates iff (7) p0 (x + 1) > α.

3 The Model

11

If it is worthwhile fighting when one’s own life is at stake, then this condition is satisfied for at least some x. This condition is the same as (1); as all players’ payoffs are identically shared in this situation, the efficient solution is possible in equilibrium. Suppose that p0 (1) < α. This fits our intuition that fighting alone against overwhelming odds is pointless. We then have: Proposition 1. If and only if p0 (m) ≥ α for some m ∈ {0, 1, ..., m}, ¯ then for δ close enough to 1, there is an equilibrium in which all players cooperate when m players are left. In other words, whenever cooperation is efficient from the point of view of the group, it can take place in equilibrium. The proof is in the appendix. The intuition is straightforward: at any group size less than m, there is no cooperation. Therefore, the penalty for losing at m is certain death after at most m rounds; for sufficiently patient players, this is like the situation described above, where a single round of conflict decides all players’ fate. The dynamics thus makes a Stag Hunt out of the original collective action problem, which had a Prisoner’s Dilemma-like structure. The condition p0 (1) < α but p0 (m) ≥ αfor some m > 1 suggests that p(·) may be convex. This can be justified by Lanchester’s Square Law (Lanchester, 1916), originally developed during the Great War to understand artillery combat. If two sides are fighting, the larger side gains both because it has more firepower, and can kill the other side faster, and because it is larger and can take more damage. The strength of each side is thus proportional to the square of its numbers. If the enemy has a fixed size y, then √ 2 p(x) = x2x+y2 would be an appropriate conflict function. This is convex for x < y/ 3. This proposition does not say that every equilibrium has cooperation – given p0 (1) < α, it is always in equilibrium for nobody to cooperate. It also does not say there is any equilibrium such that whenever p0 (m) ≥ α, all players cooperate. That will in general be false. If all cooperate when m are left, then cooperation is unlikely at m+1, since the price of failure is not certain death, but instead the death of a single member followed by another chance to beat the enemy. In general the “most cooperative” equilibria involve cooperation at a set of values of m spaced far away enough from each other to make cooperation worthwhile. This is discussed further in Subsection 6.2 of the appendix. It is also not strictly necessary that p0 (1) < α. If p0 (m) > α for m ∈ {1, ..., m} ¯ then there may be cooperation at m = 1. This then reduces the benefit of cooperation. The next highest place at which cooperation takes place has to satisfy (for δ arbitrarily close to 1): 1 p0 (m)[1 − p(1)] ≥ α (8) m where p(1) = p0 (1) since p(0) = 0. Thus, if this holds for some lowest m, there will be an equilibrium in which all m cooperate at m and thereafter not until m = 1. Finally, it is worth comparing this explanation with “punishment” explanations for cooperation. As noted above, punishment in these cases just means that other people

4 A simple model with a single attacker

12

withdraw future cooperation. Here, too, failing to cooperate can lessen future cooperation from others, not because they are playing a conditional strategy, but because they are killed. (Cf. Eshel, Samuelson and Shaked (1998); Eshel and Shaked (2001).) Both arguments depend on sufficiently high patience. This is a weakness – the shadow of the future may be short during violent episodes – but also suggests interesting comparative statics, since δ may be endogenously manipulable by the opponent. A key difference with punishment explanations is that they lead players to Defect when this is unobservable, whereas the setup here incentivizes even unobservable cooperation.

4 A simple model with a single attacker To show that the conflict of interest between participants on one side has substantive consequences, I simplify the model considerably and introduce some changes. Suppose now that N = 2. As before, either player can cooperate at a cost of α to fight off an external attacker. The attacker is now strategic and can choose whether or not to attack when there are m = 2 or m = 1 opponents left. If the attacker loses, the game simply continues. If the attacker beats an opponent, he gets booty of 1. We now reinterpret 1 − δ as the probability that a player can escape the conflict, either by flight, or by “passing” as one of the attackers (Kalyvas, 2008). When this happens, the attacker gets booty of 0 ≤ b ≤ 1, while the player retains x = 1 − b. Finally, we represent p(·) by two numbers: q is the probability that the players win when only one cooperates; p is the probability that the players win when both cooperate. As before, there are infinite rounds and we seek Markov strategies. Attacking is costless and as it generates a positive probability of winning 1 rather than b, it is a dominant strategy at m = 2 and m = 1, so the attacker always attacks. Since the players always eventually escape or die, escaping is also a dominant strategy. We describe the players’ cooperation strategies as follows: both players play C with probability σ when m = 1, while their probabilities of playing C at m = 2 are denoted σ1 and σ2 respectively.

4.1 The players' optimal strategies 4.1.1

At

m=1

We can write either player’s value of cooperation as V1C = −α + q[(1 − δ )x + δV1 ]

(9)

and of defection as V1D = 0, where V1 = max{V1C ,V1D } is the value of the game at m = 1. Thus, σ = 1 iff −α + q(1 − δ )x ≥0 (10) V1 = V1C = 1 − qδ i.e. if α ≤ q(1 − δ )x (11) .

4 A simple model with a single attacker

13

Condition p−q α ≤ 1−δ 2q Z

α≥

Round 2 behaviour CC is an equilibrium

p−q Z 1−δ 2 q

and α ≤ qZ α ≥ qZ Tab. 2:

4.1.2

At

CD or DC is an equilibrium DD is an equilibrium

Equilibrium conditions

m=2

Table 2 on page 13 describes the possible equilibria, where Z = (1 − δ )((1 − δ )δV1 + (1 + δ 2 )x)/2.

(12)

p−q 2 The proof is in the appendix. If 1−δ 2 q < q (equivalently, p < (2 − δ q)q, which is strictly tighter than concavity), then the parameters determine a unique equilibrium number of cooperators, which may be 0, 1 or 2. Otherwise, there are 0 or 2 cooperators, p−q and for α ∈ [qZ, 1−δ 2 q Z] there are multiple equilibria.

4.2 Comparison: a unied group Suppose now that the two group members’ strategies are determined by a single group decision-maker who maximizes the sum of both members’ utilities. (We could alternatively assume a cooperative bargaining process.) This will provide a useful benchmark to show the difference made by the non-cooperative game between group members. Clearly, the decision at m = 1 is unchanged and is determined by (11). (In other words, I do not assume that a unified group can commit any better than the individuals can.) Decisions at m = 2 are as follows. Define 2(p − q) Z; 1 − δ 2 (2q − p) pZ;

α1

=

α2

=

α3

= 2qZ

(13) (14) (15)

, where Z is defined as in the previous sectionIf p > 2q, i.e. the function is convex, then the group decision-maker plays CC if α < α2 and DD otherwise. If p ≤ 2q then the decision-maker plays CC if α < α1 , CD (or DC indifferently) if α ∈ [α1 , α3 ] and DD if α > α3 . The proof is in the appendix.

4.3 Application: the value of a second line of defence With these two solutions, we can examine comparative statics. One interesting question is: holding other parameters constant, what happens if we vary q? An increase

4 A simple model with a single attacker

Fig. 1:

14

Value of the game by q. The solid line shows one possible non-cooperative equilibrium. The dashed line shows the efficient choice of a unified decisionmaker. In the leftmost region, there are multiple equilibria for the divided (noncooperative) solution; anything between the dashed and solid line is possible. On the right, as q increases it causes one defender to inefficiently shift from C to D. (Parameters: p = 0.8, δ = 0.85, x = 0.5, α = 0.24.)

in q means that the second stage of any attack becomes more difficult for the attacker, holding the choices of the defenders constant, perhaps because defence becomes easier when defenders are harder to locate, or because there are a limited number of good defensive locations. Intuitively, one would expect an increase in q to benefit the defenders, and indeed this holds if the group is unified: writing V UNIF for the value to the defenders in this case, we have V UNIF is weakly increasing in q. (The proof is in the appendix.) But this result can be overturned when the defenders choose separately. For a stronger second line of defence may exacerbate the collective action problem of the defenders in the first round. Figure 1 on page 14 shows an example. Here, at a certain level of q, it is no longer individually rational for both defenders to cooperate at m = 2, even though this would maximize their survival chances. Stronger defence technology can thus make a group worse off.

5 Conclusion

15

4.4 Application: social construction of group identity Suppose that N = 3, but that the attacker can only ever attack two of the three defenders, due to resource or geographical constraints. Also, the attacker must announce his choice at the start of the game, perhaps because the attacker’s supporters must publicly coordinate on a target. Trivially, only group members who are declared as targets will play Cooperate. This is the simplest model of the social construction of group identity. The attacker’s choice of targets can then be examined. If every choice gives a particular p and q, then the previous section shows that the “weakest” targets, in terms of the defence technology, will not always be chosen: a small increase in q may shift defenders’ cooperation levels sharply downwards. Another issue is the attacker’s commitment problem. If p(·) is highly convex, it may be advantageous to target only a subset of defenders, but it will be hard to persuade the others that they will not be targeted later. Therefore, attackers need ways of commiting to limited aggression. Horowitz (2001) notes the extreme care taken by rioters to avoid accidental harm to non-members of the targeted outgroup. We might also expect ethnic boundaries – the ability of groups to “pass”, modelled above as 1 − δ – to be manipulated so that some groups can feel secure from attack while others are singled out.

5 Conclusion It is widely thought that conflict participation cannot be rational, but this is not necessarily the case. Even participants uncoerced by their own side, and outside of long-term relationships which might incentivize cooperation, may fight if by doing so they further their own long-term survival. Furthermore, rational participation can explain the symbolic aspects of violent conflict – the struggle over national or ethnic symbols, the cruelty and humiliation inflicted – as well as the material aspects. Here, I describe some future research topics that seem promising, starting on the formal-theoretic side. The most pressing need is to model the attacker’s choices more fully, i.e. to fill in the other side of the contest function p(·). The case of a single attacker is interesting, since conflicts are often asymmetric, with a unified state facing decentralized opposition. One variable under the attacker’s control may be δ . Maximizing δ is unlikely to be optimal, since this will increase defenders’ cooperation levels. Interpreting δ as the speed of an attack will lead to one set of empirical predictions. (For example, it is suggestive that the Nazi genocide, using advanced technology, proceeded more slowly than the genocide in Rwanda using machetes.) Another interpretation, as mentioned, is that 1 − δ gives the ability of minority group members to “pass” temporarily or permanently into the majority coalition. The ethnic boundaries in Caselli and Coleman (2006) can then emerge endogenously, in accordance with the widespread view that these boundaries are symbolically or socially constructed (Anderson, 1991; Cohen, 1986). The case of two groups in conflict is also important. Modelling the motivational asymmetry between defenders and attackers mentioned in Subsection 1.1 could give

6 Appendix

16

predictions on which ethnic population structures will be stable. It may also throw new light on the ethnic security dilemma, by showing when intergroup conflict will be localized and when it will become more general. Finally, surprising evidence of cooperation even in short-term situations (e.g. Guth, Schmittberger and Schwarze, 1982) has led some social scientists to develop evolutionary models of human altruism (reviewed in Nowak, 2006). These often have an element of group selection, which usually occurs exogenously (e.g. Boyd et al. 2003). Introducing endogenously chosen group conflict might lead to new insights into “parochial altruism” (Choi and Bowles, 2007). If human groups have regularly faced violence in the past, we can expect their psychology, whether evolved or learned, to reflect the objective incentives of the situation. (Proponents of Realistic Conflict Theory, Reciprocity Theory and Social Dominance Theory all make similar arguments.) From the model above, then, we could make predictions on the social psychology of outgroup prejudice and ingroup support. These predictions will differ from Realistic Conflict Theory, which makes predictions directly from group interests, Reciprocity Theory, which focuses on the mutual provision of benefits within a group without reference to outsiders, and Social Dominance Theory, which sees stratification in a large society as fundamental. In addition to modelling work, I believe that developing these social psychology predictions, and testing them experimentally, will provide an interesting research agenda.

6 Appendix 6.1 Proof of Proposition 1 “Only if” is easy: if p0 (m) < α then it can never be worthwhile for all m players to cooperate since the gain from doing so is at most p0 (m) (the extra probability of winning from the marginal cooperator) times 1 (the difference between certain survival and certain death), and the cost is α. To show “if”: the utility of cooperation when m players are left is   m−1 Vm−1 UC (m) = (1 − δ ) − α + δ p(x + 1)1 + (1 − p(x + 1)) m

(16)

where x gives the number of other players playing C, and the utility of defection is:   m−1 UD (m) = (1 − δ ) + δ p(x) + (1 − p(x)) Vm−1 (17) m so that a player plays C iff m−1 Vm−1 ] ≥ α/δ . m Thus an equilibrium in which exactly x players cooperate satisfies [p(x + 1) − p(x)][1 −

p0 (x)[1 −

m−1 Vm−1 ] ≥ α/δ m

(18)

(19)

6 Appendix

17

and this fails to hold for numbers above x if x < m. We consider the following equilibrium: all defect when m0 6= m players are left, while all m players cooperate when m players are left. Since p0 (1) < α clearly universal D . As δ → 1, V D → 0 and defection is a possible equilibrium. Therefore, Vm−1 = Vm−1 m−1 0 the above equation goes to p (x) ≥ α, which is satisfied for x = m.

6.2 The form of equilibria Holding δ fixed for the moment, and assuming p convex on the relevant interval, the lowest possible m at which cooperation is possible satisfies m−1 D V ] = α/δ . (20) m m−1 (assuming innocuously that this equality holds for some integer value of m). What about at m + 1? First we calculate   m−1 D Vm = (1 − δ ) − α + δ p(m) + (1 − p(m)) Vm−1 (21) m p0 (m)[1 −

with Vm → −α + p(m) as δ → 1. The condition for cooperation is now  p0 (m + 1) 1 −

m Vm m+1

(22)

 > α/δ .

(23)

(Using convexity of p, if this condition is not satisfied for p0 (m + 1) it will not be satisfied for any lower number of cooperators.) Once again taking δ → 1, this approaches   m (p(m) − α) > α. (24) p0 (m + 1) 1 − m+1 Recalling the definition of p0 (m) as p(m) − p(m − 1), and that p0 (m) → α as δ → 1, we know that p(m) > α (assuming m > 1), so that the term in parentheses is less than 1. Compared to (20), which reduces to p0 (m) = α as δ → 1, this condition requires that p0 (m + 1) be strictly larger than p0 (m). If p0 does not change very fast between m and m + 1, so that (24) will not be fulfilled, we examine m + 2, where the condition become   m+1 p0 (m + 2) 1 − Vm+1 > α/δ , (25) m+2 and where we can calculate Vm+1 = (1 − δ ) + δ

m m Vm → Vm as δ → 1; m+1 m+1

(26)

6 Appendix

18

thus our condition for δ close to 1 approaches   m p0 (m + 2) 1 − Vm > α. m+2

(27)

This logic can be continued indefinitely, and, writing m1 ≡ m, we conclude that the next place where some cooperation is possible in equilibrium ism2 satisfying   m1 0 (28) p (m2 ) 1 − Vm1 = α. m2 So long as p remains convex, the whole process can then be repeated to give m3 satisfying   m2 0 p (m3 ) 1 − Vm2 = α (29) m3 where Vm2 → −α + p(m2 ) + (1 − p(m2 ))

m1 Vm as δ → 1 m2 1

(30)

and so forth. In general, then, as δ → 1 cooperation occurs only at discrete points m1 , m2 , m3 , . . . satisfying   mi−1 Vmi−1 = α p0 (mi ) 1 − (31) mi where Vmi = −α + p(mi ) + (1 − p(mi ))

mi−1 Vmi−1 ; mi

(32)

and at each of these points all surviving players cooperate. Cooperation at any of these points is rather fragile. Since p is convex, if a single player were to deviate and play Defect then it would be rational for all others to do so. As mentioned in the text, the fragility of cooperation in group defence provides a plausible explanation for the role of group humiliation in ethnic conflict. There are other equilibria. For example, it might be that no players cooperate when there are m1 players remaining; since p is convex, if no other players cooperate then cooperation is irrational for any individual, so this is an equilibrium. Instead, m1 or m1 + 1 players may cooperate when there are m1 + 1 players remaining. Further points of cooperation would then have Vk defined by the value of cooperation at m + 1 (and defection up to and after that point). These equilibria are less unstable: for example, if all players cooperate when m1 + k remain, then this equilibrium is robust to the defection of up to (approximately)k players. Nevertheless, it is always an equilibrium for nobody to cooperate.

6 Appendix

19

6.3 Derivation of equilibrium strategies when m = 2 Let i ∈ {1, 2} and j = 3 − i. Then player i’s value of cooperation is Vi2C = −α + Pj [(1 − δ )x + δ (1 − δ )V1 + | {z } | {z } i escapes

j escapes

δ 2V | {zi2}

] + (1 − Pj ) ((1 − δ )x + δV1 )/2 {z } |

neither escape

one player killed

(33) and of defection, Vi2D = qσ j [(1 − δ )x + δ (1 − δ )V1 + δ 2Vi2 ] + (1 − qσ j )((1 − δ )x + δV1 )/2

(34)

max{Vi2C ,Vi2D }

where Vi2 = and Pj = σ j p + (1 − σ j )q is the probability of winning, depending on j’s strategy. Rearranging, the condition for σi = 1 is that Vi2 = Vi2C =

−α + (1 − Pj )((1 − δ )x + δV1 )/2 + Pj (1 − δ )(δV1 + x) 1 − δ 2 Pj

(35)

and that this is greater than Vi2D . Solving this latter inequality for α gives α≤

(1 − δ )(Pj − qσ j )((1 − δ )δV1 + (1 + δ 2 )x)/2 1 − δ 2 qσ j

(36)

. Suppose σ j = 1. If σi = 1 is a best response then by symmetry σi = σ j = 1 is in equilibrium. The condition for this is given by plugging Pj = p and σ j = 1 into the above: (1 − δ )(p − q)((1 − δ )δV1 + (1 + δ 2 )x)/2 α≤ (37) 1 − δ 2q . Suppose σ j = 0. If σi = 0 is a best response then again we have an equilibrium by symmetry. If σi = 1 is a best response then for an asymmetric equilibrium we require also that (37) is violated. The condition for σi = 1 to be a best response is given by plugging Pj = q and σ j = 0 into (36): (1 − δ )q((1 − δ )δV1 + (1 + δ 2 )x)/2 . (38) 1 This and the previous inequality give us the results in Table 2 on page 13, once we have substituted in Z = (1 − δ )((1 − δ )δV1 + (1 + δ 2 )x)/2. α≤

6.4 Derivation of the unied decision-maker's strategy The decision maker chooses a strategy out of {CC,CD,DC,DD} to maximize the total value of the game. CD and DC are obviously equivalent when the 2 players’ utilities are summed. We write out the value of the game for 2, 1 and 0 cooperators respectively as V CC

= −2α + p[(1 − δ )2 2x + 2δ (1 − δ )(x +V1 ) + δ 2V CC ] + (1 − p)[(1 − δ )x + δV (39) 1]

V CD

= −α + q[(1 − δ )2 2x + 2δ (1 − δ )(x +V1 ) + δ 2V DC ] + (1 − q)[(1 − δ )x + δV(40) 1]

V DD

= (1 − δ )x + δV1

(41)

6 Appendix

20

and solve for V CC and V CD : V CC

=

V CD

=

−2α + δ (1 + p − 2δ p)V1 + (1 − δ )(1 + p)x 1−δ2p −α + δ (1 + q − 2δ q)V1 + (1 − δ )(1 + q)x 1 − δ 2q

(42) (43)

Solving the three resulting inequalities gives 2(p − q) Z ≡ α1 1 − δ 2 (2q − p)

V CC ≷ V CD

⇔ α≶

V CC ≷ V DD

⇔ α ≶ pZ ≡ α2

(45)

⇔ α ≶ 2qZ ≡ α3

(46)

V

CD

≷V

DD

(44)

whereZ = (1 − δ )((1 − δ )δV1 + (1 + δ 2 )x)/2 as before. Algebra shows that if p > 2q, α1 > α2 > α3 and if p < 2q, α1 < α2 < α3 , leading to the behaviour described in the text.

6.5 Proof that value increases in q for a unied decision maker Write V UNIF = max{V CC ,V CD ,V DD }. V CC and V DD depend on q only via V1 , and are increasing in V1 . −α + q(1 − δ )x V1 = max{0, } (47) 1 − qδ from (10). Observe that V1 ≤ Differentiating

−α+q(1−δ )x 1−qδ

q(1 − δ )x < x. 1 − qδ

(48)

with respect to q gives δ (−α + q(1 − δ )x) (1 − δ )x + (1 − qδ )2 1 − qδ

(49)

and this is positive whenever q(1 − δ )x > α, i.e. whenever V1 is not constant at 0, so V1 is weakly increasing in q. Thus, V CC and V DD are increasing in q, and we need only check V CD . I show that for any parameter values such thatV CD decreases in q, V CD < V DD . Suppose first that V1 is constant at 0, for a given value of q. Then differentiating (43) gives ∂V CD ∂q

=

2(1 − δ )2 x + (δ 2 + 2δ − 1)(1 − δ )x − αδ 2 (1 − δ 2 q)2

(50)

=

(1 − δ )(1 + δ 2 )x − αδ 2 . (1 − δ 2 q)2

(51)

6 Appendix

If V1 =

−α+q(1−δ )x 1−qδ

21

> 0, then since V CD is increasing in V1 which is increasing in q,

(51) is a lower bound for

∂V CD ∂q .

(51) is negative iff α>

and so in general we have

∂V CD ∂q

(1 − δ )(1 + δ 2 )x δ2

(52)

< 0 only if (52) holds, which in turn implies

α > (1 − δ )(1/δ 2 + 1)x > (1 − δ )2x

(53)

Now for V CD ≥ V DD we require α

≤ α3 = 2qZ < 2Z = (1 − δ )[(1 − δ )δV1 + (1 + δ 2 )x] ≤ (1 − δ )[(1 − δ )δ x + (1 + δ 2 )x] by (48) = (1 − δ )(1 + δ )x < (1 − δ )2x

and since this contradicts (53), we have shown that completing the proof.

(54) ∂V CD ∂q

< 0 implies V CD < V DD ,

References Acemoglu, D. and J. A Robinson. 2006. Economic origins of dictatorship and democracy. Cambridge University Press. Anderson, B. 1991. “Imagined Communities: Reflections on the Origin and Spread of Nationalism, rev. ed.” London and New York: Verso 11. Bauerlein, M. 2001. Negrophobia: A race riot in Atlanta, 1906. Encounter Books. Beber, B. and C. Blattman. N.d. “The Industrial Organization of Rebellion: The Logic of Forced Labor and Child Soldiering.” . Forthcoming. Bernhard, H., U. Fischbacher and E. Fehr. 2006. “Parochial altruism in humans.” Nature 442(7105):912–5. Blattman, C. and E. Miguel. 2008. “Civil war.” forthcoming in Journal of Economic Literature . Boix, C. 2003. Democracy and Redistribution. Cambridge University Press. Bouckaert, J. and G. Dhaene. 2004. “Inter-ethnic trust and reciprocity: results of an experiment with small businessmen.” European Journal of Political Economy 20(4):869–886.

6 Appendix

22

Boyd, R., H. Gintis, S. Bowles and P. J. Richerson. 2003. “The evolution of altruistic punishment.” Proceedings of the National Academy of Sciences 100(6):3531–3535. Brewer, Marilynn B. 1999. “The Psychology of Prejudice: Ingroup Love or Outgroup Hate?” Journal of Social Issues 55(3):429. Campbell, D. T. 1965. Ethnocentric and other altruistic motives. In Nebraska symposium on motivation. Vol. 13 p. 283–311. Caselli, F. and W. J Coleman. 2006. On the Theory of Ethnic Conflict. Cambridge, Mass.: National Bureau of Economic Research. Chen, Y. and X. Li. 2006. Group Identity and Social Preferences. Published: Unpublished. Choi, J. K and S. Bowles. 2007. “The Coevolution of Parochial Altruism and War.” Science 318(5850):636. Chong, D. 1991. Collective Action and the Civil Rights Movement. Chicago: University Of Chicago Press. Cohen, Anthony P. 1986. Symbolizing Boundaries: Identity and Diversity in British Culture. Manchester University Press. Dawes, R. M. 1980. “Social dilemmas.” Annual review of psychology 31(1):169–193. Eshel, I. and A. Shaked. 2001. 208(4):457–474.

“Partnership.” Journal of Theoretical Biology

Eshel, I., L. Samuelson and A. Shaked. 1998. “Altruists, egoists, and hooligans in a local interaction model.” American Economic Review pp. 157–179. Fearon, J. D. and D. D. Laitin. 1996. “Explaining interethnic cooperation.” American Political Science Review pp. 715–735. Fearon, J. D. and D. D. Laitin. 2003. “Violence and the social construction of ethnic identity.” International Organization 54(04):845–877. Fershtman, C. and U. Gneezy. 2001. “Discrimination in a Segmented Society: an Experimental Approach.” Quarterly Journal of Economics 116(351-377). Garay, J. 2008. “Cooperation in defence against a predator.” Journal of Theoretical Biology . Goette, L. and D. Huffman. 2006. The Impact of Group Membership on Cooperation and Norm Enforcement Evidence Using Random Assignment to Real Social Groups. IZA. Gourevitch, P. 1999. We wish to inform you that tomorrow we will be killed with our families: Stories from Rwanda. Picador.

6 Appendix

23

Guth, W., R. Schmittberger and B. Schwarze. 1982. “An experimental analysis of ultimatum bargaining.” Journal of Economic Behavior and Organization 3(4):367–388. Habyarimana, James, Macartan Humphreys, Daniel Posner and Jeremy Weinstein. 2007. “Why ethnic diversity undermine public good provision.” American Political Science Review 101:709–725. Halevy, N., G. Bornstein and L. Sagiv. 2008. “In-Group Love and Out-Group Hate as Motives for Individual Participation in Intergroup Conflict: A New Game Paradigm.” Psychological Science 19(4):405–411. Hamilton, W. D. 1971. “Geometry for the selfish herd.” Journal of Theoretical Biology 31(2):295–311. Hardin, R. 1995. One for All: The Logic of Group Conflict. Princeton: Princeton University Press. Hargreaves-Heap, S. and Y. Varoufakis. 2002. “Some experimental evidence on the evolution of discrimination, co-operation and perceptions of fairness.” Economic Journal pp. 679–703. HEAP, SPH and DJ ZIZZO. N.d. “The Value of Groups.” . Forthcoming. Hewstone, M., M. Rubin and H. Willis. 2002. “I NTERGROUP B IAS.” Annual review of psychology 53(1):575–604. Hobbes, T. 1651. Leviathan. Horowitz, D. L. 2001. The deadly ethnic riot. University of California Press. Jervis, R. 1978. “Cooperation under the security dilemma.” World Politics: A Quarterly Journal of International Relations pp. 167–214. Kalyvas, S. N. 2008. “Ethnic Defection in Civil War.” Comparative Political Studies 41(8):1043. Kaufman, S. J. 2001. Modern Hatreds: The Symbolic Politics of Ethnic War. Cornell University Press. Kinder, D. R. and D. O. Sears. 1981. “Prejudice and politics: Symbolic racism versus racial threats to the good life.” Journal of Personality and Social Psychology 40(3):414–31. Kuran, T. 1998. “Ethnic norms and their transformation through reputational cascades.” The Journal of Legal Studies 27(S2):623–659. Lake, D. A. and D. Rothchild. 1996. “Containing fear: The origins and management of ethnic conflict.” International Security pp. 41–75. Lanchester, F. W. 1916. Aircraft in warfare: The dawn of the fourth arm. Constable and company limited.

6 Appendix

24

Locke, J. 1988. Two treatises of government. Cambridge University Press. McLeish, K. N. and R. J. Oxoby. 2007. Identity, cooperation, and punishment. IZA. Mueller, J. 2000. “The Banality of "Ethnic War".” International Security pp. 42–70. Mummendey, A., B. Simon, C. Dietze, M. Grünert, G. Haeger, S. Kessler, S. Lettgen and S. Schäferhoff. 1992. “Categorization is not enough: Intergroup discrimination in negative outcome allocation.” Journal of experimental social psychology(Print) 28(2):125–144. Nowak, M. A. 2006. 314(5805):1560.

“Five Rules for the Evolution of Cooperation.” Science

Oberschall, A. 2000. “The manipulation of ethnicity: From ethnic cooperation to violence and war in Yugoslavia.” Ethnic and Racial Studies 23(6):982–1001. Oberschall, A. 2001. “From ethnic cooperation to violence and war in Yugoslavia.” Ethnopolitical warfare: Causes, consequences, and possible solutions p. 119–150. Ostrom, Elinor, James Walker and Roy Gardner. 1992. “Covenants With and Without a Sword: Self-Governance is Possible.” The American Political Science Review 86(2):404–417. ArticleType: primary_article / Full publication date: Jun., 1992 / c 1992 American Political Science Association. Copyright URL: http://www.jstor.org/stable/1964229 Petersen, R. D. 2002. Understanding Ethnic Violence: Fear, Hatred, and Resentment in Twentieth-Century Eastern Europe. Cambridge University Press. Popkin, S. L. 1979. The rational peasant: The political economy of rural society in Vietnam. University of California Press. Posen, B. R. 1993. “The security dilemma and ethnic conflict.” Survival 35(1):27–47. Sherif, M., O. J. Harvey, B. J. White, W. R. Hood and C. W. Sherif. 1961. The Robbers Cave experiment: Intergroup conflict and cooperation. Wesleyan University Press Scranton, Pa.: Distributed by Harper & Row, Middletown, Conn. Sidanius, J. and F. Pratto. 1999. Social dominance: An intergroup theory of social hierarchy and oppression. Cambridge University Press. Simmel, G. 1955. Conflict. Free Press New York. Stephan, W. G. and C. W. Stephan. 2000. An Integrated Threat Theory of Prejudice. In Reducing prejudice and discrimination: The Claremont symposium on applied social psychology. Lawrence Erlbaum p. 23. Stephan, Walter G., C. Lausanne Renfro, Victoria M. Esses, Cookie White Stephan and Tim Martin. 2005. “The effects of feeling threatened on attitudes toward immigrants.” International Journal of Intercultural Relations 29(1):1–19. URL: http://www.sciencedirect.com/science/article/B6V7R-4G94HSF1/2/842939d987b157235d11fd27b778c2bd

6 Appendix

25

Sumner, W. G. 1906. Folkways: A study of the sociological importance of usages, manners, customs, mores, and morals. Ginn. Tajfel, H. 1982. “Social psychology of intergroup relations.” Annual review of psychology 33(1):1–39. Tajfel, H., M. G Billig, R. P Bundy and C. Flament. 1971. “Social categorization and intergroup behavior.” European Journal of Social Psychology 1(2):149–178. Whitt, S. and R. K Wilson. 2007. “The Dictator Game, Fairness and Ethnicity in Postwar Bosnia.” American Journal of Political Science 51(3):655–668. Yamagishi, T. and T. Kiyonari. 2000. “The Group as the Container of Generalized Reciprocity.” Social Psychology Quarterly 63(2):116–132. contains references to literature on in-group favoritism in 2 person PDs.