Evolutionary Models and Third Party Intervention in Ethnic Conflict
Evolutionary Models and Third Party Intervention in Ethnic Conflict
David Carment & Dane Rowlands
The Norman Paterson School of International Affairs
The purpose of the paper is to develop and evaluate an evolutionary game theoretic approach to explain third party intervention into ethnic conflict. Specifically, the evolutionary approach developed here takes into account the long-term repeated interactions of players involved in third party intervention scenarios both within and between conflicts. A modified version of Kreps' "Quiche" game forms the basis for one of the models, with a second relying on the "replicator" approach. The analysis highlights the importance of learning, reputation, chance, and path dependence in determining successful third party intervention. Implications for intervention into ethnic conflicts in the post-Cold War period are assessed.
1. Introduction <1>
Struggles involving civil wars, secessions and ethnic violence far outnumber those stemming from external aggression or conflict between states, especially in recent years. These internal conflicts over identity, government and territory, are arguably more difficult to resolve through peaceful negotiation than their interstate counterparts. As a consequence of these recent developments there have been fundamental changes in the nature of third party intervention. During the Cold War, a period of unprecedented stability in this century, many internal conflicts were contained because their diffusion represented a potentially destabilizing effect on East-West relations. Other, less salient conflicts were left to languish on the sidelines.
Today there is a heightened sense of collective responsibility to respond to internal conflicts, small and large, based on the fear that many conflicts will lead to internal instability or worse; non-combatants are at risk of large-scale violence; armed militias, generally operating outside the purview of traditional authority structures, endanger post-conflict stability. Many internal conflicts spillover into the international domain, making greater complexity an additional drain on overburdened crisis-management resources. Potential sources of diffusion and escalation range from refugee flows to terrorism.
To be sure, the Cold War provided the legal and political context for managing today's global and regional threats to security. However, most multilateral interventions during this 45 year period were intended only to deter recurring interstate frictions. In this context, multilateral forms of third party intervention were designed to monitor ceasefire arrangements after two warring states had reached a negotiated settlement or ceasefire. This basic reference point has now shifted, as new states have emerged on the scene and the bulk of conflicts are now internally generated. In the post Cold War era, new states bring with them unresolved ethnic tensions and political and territorial problems. In grappling with these security threats, Article 2(7) of the United Nations charter states that the UN should not intervene in matters that are essentially within the domestic jurisdiction of any state. However, "the charter shall not prejudice the application of enforcement measures under Chapter VII." That is, if a domestic conflict is construed as a threat to international peace and security then the United Nations Security Council may sanction a mandate to intervene.
On the one hand, with the importance of the Cold War rivalry reduced significantly, the opportunity to intervene forcefully has increased dramatically. On the other hand, with the loosening of ideological bonds and the commensurate weakening of state-centres aided by foreign governments, bloody civil wars have returned with a renewed vengeance. Given past restrictions on activities in internal conflict, it becomes self-evident why it is important to understand the consequences of these two changes for the evolution of third party intervention and the management of ethnic conflicts.
The research agenda for this paper is, in the first instance, to assess the usefulness of evolutionary game theory for modelling intervention into ethnic conflict. Secondly, we identify the kinds of intervention equilibria that arise, and specify those conditions. Thirdly, the value of different strategies in generating preferred outcomes are identified. Finally, the model is used to replicate the changes in the international system as outlined in the introductory paragraph. We begin by applying static models of intervention to an evolutionary framework of analysis. We then move to a dynamic replicator model of third party intervention. This two-fold approach provides several advantages. First, it allows us to identify the conditions necessary for the successful reduction of tensions at different points in the life of a conflict. It also allows us to show how learning behaviour among ethnic belligerents has meaning not only within specific conflicts but between them. It is not enough for a third party to develop a strategy for the management of a single conflict. Belligerents observe the kinds of conflictual behaviour around them and learn from the mistakes of other challengers. In preparing to meet such challenges, third party interveners must be highly flexible, adaptive and above all selective in their choice of a strategy.
2. Understanding Intervention in Ethnic Conflict: Insights from Theory
In this section of the paper we assess the strengths and shortcomings of several existing conflict management frameworks in order to explain the process and content of third party intervention. One of the first attempts to informally model third party intervention was Zartman's (1989) influential assessment of successful mediation strategies. His concept of the "hurting stalemate" is an important contribution to the literature on third party involvement in conflict, but it is an idea which seems to suggest that such involvement will only be effective when a "ripe moment" exists. This ripe moment occurs when there is a mutually hurting stalemate, where unilateral solutions are blocked and when the parties recognize that continuing violence will damage all sides. He claims that:
Conceptually, the moment stands out, but in reality it is buried in the rubble of events.... Like any metaphor, the idea of the ripe moment should not be taken too literally. Moments, when ripe, do not fall into one's hands; they have to be taken with skill.... Thus, for the conciliating power, it is a question not only of correctly identifying the right times to move but also of moving the times with skill (Zartman 1989: 273).
In essence, Zartman argues that the elimination of alternative regimes by the groups in conflict, the readjustment of power relations between these groups, and the identification of a ripe moment are necessary for successful conflict reduction.
Zartman's insights are useful for two reasons. First his model suggests that third parties can, in theory, induce ripe moments through the creation of hurting stalemates. With sufficient leverage third parties can reduce the likelihood of intransigence on the part of a belligerent who resists bargaining in order to seek large anticipated gains to continued conflict. Furthermore, vigorous third parties may also prevent ascendant party in a conflict from imposing unilateral solutions. One implication of the idea of the hurting stalemate is that constructive involvement before this point in the conflict is reached is not likely to be fruitful. However, with the prospect that one party might be eliminated (or at least have its power sufficiently reduced) by a third party, ethnic groups would, in theory, be more open to a negotiated solution as opposed to continued war. Third parties can speed up the movement toward negotiation through the imposition of deadlines and other crisis-related strategies in order to decrease the perceived attractiveness of military options. Thus, the emergence of a resolving formula follows on a readjustment of the belligerents' power relations and the elimination of alternative strategies through concerted coercive efforts by third parties.
Following on Zartman's concept of timing, phase-based approaches to third party intervention build on the work of Kriesberg (1997), Lund (1996), Dixon (1996), Brecher (1994) and Bercovitch (1996), among others. Collectively, they draw attention to the fact that conflicts occur through cycles in which different third party strategies are more likely to be effective than others at different points in a conflict. This insight has both empirical and theoretical validity. Empirically, it is extremely unusual for a single strategy to be implemented over the life of a civil war. In the context of internal conflicts, rare is the intervention where third parties have not relied on some form of coercive diplomacy to bring the belligerents to the negotiating table. Intervention does not refer simply to the physical presence of a "managing agent" intent on using coercion to dissuade belligerents from using force to solve their differences (Dixon 1996:358). For example, in his assessment of a range of cases that extend beyond internal conflicts, Dixon (1996) concludes that, in any given conflict, third parties will generally employ as many different strategies as possible, including economic and military initiatives. These findings suggest that intervention into internal conflicts encompasses both pacific and coercive strategies.
Theoretically, phase-based approaches highlight the fact that in internal conflicts, especially ethnic ones, the main impediments to negotiated solutions consist of strategic and structural factors that limit options, narrow choices and make compromise impossible (see Moses this volume). An important consideration when assessing these impediments to ethnic conflict resolution, is their level of complexity (see Harvey in this volume). It is not unrealistic for as many as five or more "multiple sovereignties" to be engaged in a conflict at any given time. In some instances these groups may be insurgent movements, representatives of legitimate political parties, factions within ethnic groups or clans allied on some issues and divided on others.
Ethnic conflicts are further complicated by the presence of divergent identities that evolve only very slowly. Such fundamental cleavages are most apparent in cases involving secessionist movements, an extreme form of ethnic conflict. The usual justification for extremist secessionist tendencies is repression by the state center; in the secessionists' view, the exit option is viable given the alternatives. Collective identities in politically underdeveloped societies are particularly conflict-prone because identities are derived from fundamental, incontrovertible and non-negotiable values such as language, history and religion. In turn, the development of economic and political structures in politically underdeveloped states can lead to an exclusion of ethnic minorities who believe that their values are not incorporated into state structures. Minorities who rebel are those who perceive a systematic denial by the modern state of their values, aspirations and goals (see Ross in this volume).
It is also the case that the weaker side is usually less likely than its stronger opponent to be convinced of the virtues of a negotiated solution. Consistent with Zartman's insights, the weaker side in any ethnic conflict will seek out a third party guarantor. Without some significant act of good faith from the stronger side, the weaker side is unlikely to commit to a negotiated solution. There are several reasons for this reluctance. First, getting to an agreed solution is a two step process consisting of a series of "nested political games". In situations of open hostility, minority groups will resist personal costs even if it means foregoing immediate gains. If a less powerful group is to agree voluntarily to abide by a dominant group's rules, its interests also must be assured, including safeguards that the more powerful group cannot exploit it. Indeed, it is the minority, distrustful of the interests of the majority, that ultimately determines the viability of any agreement. Unfortunately, the contractual agreements between minorities and majorities in many new states is so weak that minorities cannot be convinced that their interests are best served through accommodation.
For example, Lake and Rothchild (1995), building on the work of Fearon, argue that:
Where information failures can be mitigated by external mediators and problems of credible commitment offset, in part, by external guarantees of ethnic contracts, the ability of third parties to moderate the security dilemma is very limited. External actors can seek to raise the costs of using force, in general, and preemptive uses of force, in particular, by themselves punishing groups that strike first. Through early intervention and mediation, external actors may also be able to shape military doctrines and force structures in groups beginning to prepare for self-defense. Nevertheless, unless incentives to preempt are in place, there is little outsiders can do to mitigate the security dilemma. But they can do little to change the incentives to preempt that lead groups into the security dilemma. (Lake and Rothchild 1995: 21)
Where information deficiencies denote the centrality of third parties in helping to identify a resolving formula, problems of credible commitment point to a potential role for more robust measures. In principle, third parties can act as guarantors of new ethnic contracts in the absence of a willingness to resort to peaceful measures on the part of the belligerents. Addressing the issue within the context of UN activity, Ruggie argues that there is a need to fill the "doctrinal void" between peacekeeping and peace-enforcement. Missions which involve goals clearly beyond those of traditional peacekeeping, such as seeking to neutralize local forces and to push belligerent parties towards the negotiating table, require different strategies. Ruggie proposes that international forces be given the means and mandate to "deter, dissuade and deny" (D3) the use of force by local protagonists (Ruggie 1993). If deterrence of violence fails, Ruggie argues, deployed forces attempt to dissuade parties from continuing military activities. Failure on this level necessitates the use of force to deny any one side military victory in a conflict.
Despite their significant contribution to an understanding of third party intervention, these phase based approaches can be criticized on several grounds. First, they ignore the fundamental question of whether third parties would want to - or have to - absorb the high costs of implementing such a broad range of strategies. In sum, these approaches assume that third parties, like their ethnic counterparts, are far more farsighted than circumstances permit.
A second shortcoming in explaining how ethnic groups respond to third parties is the belief that the choice of strategy follows from an actor's evaluation of all of the possible strategies within which they must interact. However this approach cannot explain how, for example, violence emerges over time or how to manage violent interactions over time in order to reduce the probability of continued war.<2>
Third, these approaches discount the reverberations of failed policy ventures on subsequent interactions between interveners and ethnic combatants, either in the same theatre of conflict or in a separate one. With uncertainty, the outcome of one intervention can affect each side's assessment of the other. Reputations can be won and lost in a single encounter, with potentially profound effects on subsequent missions.
Finally, they underestimate the costs of third party imposed solutions. All strategies involve risk to the intervener. Doing nothing may precipitate undesirable outcomes. Forceful intervention may lead to further escalation and unnecessary costs for the intervener. Finally, a weak response may not only produce undesirable results for the third party but may also lead to further gains for belligerents in the present conflict, and in separate subsequent ones. The next section provides a discussion of evolutionary game theory, how it has been used by other researchers, and how it might be applied in the case of third party intervention ion ethnic conflict to overcome the shortcomings identified above.
3. Dynamic Models and Basic Insights
Evolutionary game theory or dynamic modelling builds on the concepts and tools of standard non-cooperative game theory. In addition to the basic notions of strategy choices, payoffs, and Nash equilibrium, evolutionary game theory has introduced ideas such as "evolutionary stability" and "replicator dynamics".<3>
The fundamental question addressed by evolutionary game theory is how particular strategies fare in a series of repeated interactions with other strategies. The basic structure of evolutionary games is to have the members of a large population endowed with a predisposition to adopt a particular strategy. Different proportions of the population, however, may have propensities to adopt different strategies. Members of the population are then randomly paired off in a non-cooperative game, and the outcomes of their competition determined. The game outcome, however, is assumed to affect the ratio of the population which adopts a particular strategy.
The evolutionary game framework necessarily has elements of uncertainty, as the large population ensures that you do not know what strategic predisposition your opponent will have. Specifically, strategies which fail to `win' with sufficient frequency will tend to disappear as a character trait in the population. In evolutionary game theory, the proportion of a population which adopts a particular strategy depends on whether it leads to a high or low payoff relative to other strategies. In its most simple form, those members who adopt an inefficient strategy either die or fail to replicate themselves, and the predisposition to adopt the strategy gradually diminishes in proportion, or disappears.
A slightly different approach to the dynamics allows agents to learn from their environment. Bayesian updating is a process by which agents can learn about the behaviour of other agents, and alter their strategy choices accordingly to maximize their expected utility under conditions of uncertainty. These situations are essentially small-population games, or repeated game scenarios, where at least one player will have information on their opponent.<4> Thus the issue of reputation becomes crucial in affecting game outcomes.
The basic process can be described heuristically. Two players with incomplete information about each other meet in a competitive game. On the basis of their incomplete information, they choose a strategy and an outcome is observed. The specific outcome may in turn be used to update beliefs about opponents, new information which both sides may try to use to their advantage in subsequent encounters (depending on the nature of the game's repetition). In the next encounter, the game's outcome will be affected by the previous game's results. Thus it is clear that a path dependence may be created, a result which may not occur in a purely evolutionary game structure due to the large number of random interactions and absence of learning about opponents.
Some researchers have already attempted to address the deficiencies of static models by garnering insights from evolutionary game theory. According to Morrow (1985) and Signorino (1996), players in evolutionary models do not optimize all their strategies but instead adopt or modify to the successful strategies they see around them. Players incorporate some mechanism for reproduction or the spreading of successful strategies. They can do so through ecological evolutionary adaptation whereby better performing strategies are those that are adopted by the population.<5>
Using territory analysis, Axelrod (1984) argues there is no single best strategy because it depends on what the other players are likely doing. Performance of each player's strategies are assessed on the basis of how it performs against its neighbours in a fixed territory. Therefore an effective strategy depends on the characteristics of a particular strategy, but also on the nature of the other strategies with which it must interact. Unlike the ecological approach, the territorial explanation, a variant of evolutionary theory, suggests that an effective strategy must be able to take into account the history of the interaction as it has developed so far against its neighbours rather than the population as a whole.<6>
Signorino (1996) illustrates how dynamic game theory can be used in the analysis of group interactions. In a model of bounded rationality, he shows how the formation of norms and construction of institutions can occur. These behavioural arrangements are reflections of the convergence of strategy choices. According to Axelrod, Morrow and Maoz (among others) the factors influencing choice of strategies in evolutionary game theory include:
1. Status hierarchies, which help identify how different players will behave, with `labels' identifying fixed characteristics before the game begins. Thus, third parties are expected to behave in certain ways, as are ethnic belligerents;
2. Reputation, which is established on the basis of previous actions;
3. Deterrence, so that when third parties are watching, the stakes of the current situation expand from those immediately at hand to encompass the influence of the current choice on the reputations of the players;
4. Conflict abatement, which is achieved through a central authority to police both sides. When this is not possible the best solution is self-policing i.e. limited provocability, wherein response is slightly less than the provocation eg. mobilization of troops in response to other troop movements.
Given these insights, it seems appropriate to explore further the use of game theory as a modelling approach for third party intervention in ethnic conflict. A simple static game of intervention is described in the next section. Subsequently, the dynamics of repeating that game are then considered.
4. Third Party Intervention Under Uncertainty
Third party intervention is modelled here as a modified version of Kreps' "Quiche" game.<7> Elements of the game described by Carment and Rowlands (1996) are also used, and they provide a detailed discussion justifying their modelling choices.<8>
The difficulty for the intervener is that while it would like to see the conflict end, it may not consider the problem to be particularly important. Thus the salience of the conflict to the intervener, relative to the costs of intervention, is the key determinant of whether or not it will eventually rise to the task, or back down, in the face of resistance. It is this underlying `relative' salience which the interveners know but the combatants do not, and which the game assigns probabilistically.<9>
When the intervener enters into the conflict, it is not clear to the combatants how committed the intervener is to sorting out the problem. The intervener can choose from two forms of intervention. In one case it can send a signal of a high degree of operational capability, for example a large and well equipped intervention force. On the other hand, the intervener can choose to send a less capable force. The costs and benefits to each strategy are clear: a strong force sends a signal that may deter a challenge, but which is expensive. A weaker force will be less expensive, but may invite confrontation. If the combatants are uncertain about the degree of the intervener's commitment, however, it may be profitable for the intervener to send a weak force into an important conflict to save on costs. Similarly, an intervener with little interest in a conflict may still choose to send in a relatively large force in the hope of securing a peaceful solution through negotiation.<10> Although the description here uses the relative size of the intervention force as the decision variable, it is important to understand that the role played by force size is as a signal only.
Having committed resources to solving the conflict, the intervener faces two possible responses from the combatants: they can resist the intervener, or they can negotiate a solution. The preference of the intervener is to have the combatants negotiate. If the combatant resists, then the intervener becomes involved in a costly confrontation which it will win if it is determined, and lose if it is not.<11> Since the intervener is assumed to be seeking a cessation of violence and the initiation of a negotiated solution, it is sensible to assume that the side which was `winning' the conflict prior to the intervention will be the most likely challenger to the intervener. Thus, for simplicity, the game is structured as a two-party interaction between the intervener and the ascendant combatant.
Upon observing the strength of the intervener, and taking into account any other information about the salience of the conflict, the combatant must choose between resisting or negotiating. Its preferred outcome is to resist and have the intervener back down, thereby creating and opportunity for it to pursue its fight against the weaker opponent. There may also be other resource and psychological advantages to this outcome, such as the gain in prestige amongst that part of the general population which is not strongly committed to either side of the conflict.
Resisting a committed intervener, however, can bring disaster. Even if the current intervention force is weak, high salience may drive an intervener to commit more resources. Assuming that the resources of the intervener are large relative to the combatants,<12> the model assumes that a committed intervener will eventually defeat a challenger, whose defiance will then be punished with the imposition of a settlement which favours the other side.
The strategy of negotiation leads eventually to a solution which the ascendant combatant ranks below the resist-and-win outcome, and above the resist-and-lose result. Thus in the presence of uncertainty, many game structures will have neither "always resisting" nor "always negotiating" as a dominant pure strategy.
Several important issues arise with our assumption about third party and ethnic group behaviour. Foremost among them is the question of whether the preferences of ethnic groups and third party interveners can be summarized in a single unitary decision making process. We base this assumption on the following three prior assumptions.
First we recognize that the decisions of third party interveners represent considerable pulling and hauling if not within each states bureaucracy then between the states themselves. Nevertheless, third party intervention is identified with a key decision-maker, be he/she the head of a coalition of like-minded states or the head of a regional or international organization such as NATO or the United Nations. For analytic convenience we can treat the choice of strategy of that decision maker as reflecting the sum total of the preferences of those whom he/she represents. A similar argument holds for ethnic elites who, out of fear of being replaced, will go along with the population they represent. Discordance between the preferences of ethnic elites and ethnic masses generally do not persist for long.
Second, before we accept the abstraction of third parties and ethnic groups as rational unitary actors we must satisfactorily specify the objectives of their decision makers. Arrow's theorem suggests that although states unified under a multilateral coalition and members of an ethnic group may act as if they are unitary decision makers, they may also act incoherently in the sense of not revealing a complete set of transitive preferences. It may be impossible to argue that any collection of persons or states is acting as if they were pursuing an identifiable goal. Nevertheless we assume that in our model they act as if they share readily discernible goals. For the third party the primary goal is the cessation of violence with minimum costs. For the ethnic belligerent the goal is maximization of gains.
Finally, although ethnic conflicts are clearly very complex (as the previous discussion has demonstrated), we maintain that the simplification to a two player game structure still yields results which are theoretically and empirically useful. The tradeoff in reducing the number players to two in any given game has both advantages and disadvantages. On the plus side, the heuristic discussion is fundamentally less complex while retaining the same core logic of conflict management. In any given interaction between a belligerent and third party there will always be an ascendant internal force relative to the other groups. This was clearly the case in Bosnia (the Serbs) and Somalia (Aideed's forces), for example. In both scenarios, conflict abatement was premised upon the assumption that peace would be impossible without first securing the ascendant group's quiescence. On the negative side of the ledger is some loss in nuance and detail. However this investigation is premised on the assumption that consequences of action are as important as their content. For example, we can look at the decision by a third party to intervene forcefully in order to prevent an ethnic belligerent from making significant gains against a weaker group, ignoring for the time being whether such intervention requires armed conflict or whether it requires a combination of economic, political and military measures.<13> With this approach we deliberately ignore the minutiae of bargaining and the precise mechanisms that third parties might employ to induce conflict reduction. The sacrifice in detail allows us to better predict outcomes of where stable equilibria occur.
In sum our basic approach consists of two decision makers - the first representing a third party coalition faced with a decision of whether and how to intervene in an ethnic conflict - the second representing the head of an ethnic belligerent group faced with a decision to resist or capitulate to that third party. Our objective is to specify the sequence of events in which each tries to maximize gains via the decisions entailed in confrontation and cooperation.
The one shot game is presented in Figure 1. As discussed, the first step in the game is the probabilistic determination of whether the intervener is prepared to commit sufficient forces to overcome resistance or, essentially, the conflict's relative salience to the intervener. At the next stage, the intervener chooses between a relatively weak or relatively strong intervention force. Having observed the intervention force's capabilities, the dominant combatant must choose whether or not to resist the intervener. Confronting a determined intervener leads to the worst outcome for the combatant. If it resists a weakly committed intervener, however, it achieves the best outcome. Negotiating leads to the same peaceful settlement regardless of the strength of the intervention force.
|FIGURE 1: The One Shot Game
The combatant's preference ordering is based on the outcome only, and is assumed to be:
E = G > B = D = F = H > A = C
The intervener's rankings are assumed to be more complex. The three determining factors are the outcome, the salience of the conflict, and the costs of the intervention (signal). We assume that it is more costly to support a weak force than a strong one when resistance occurs in a high salience conflict, and that it is better to have a negotiated solution than to have to defeat a challenge. Thus the following preference ranking is used for the intervener:
B > D > F > H > C > A > E > G.
Insights are drawn from the static game by assigning numerical values to the outcomes. The model is then solved for a pure or behavioral equilibrium, with the solution being dependent on the initial probability that the conflict is of high salience to the intervener. The game can then be solved for a range of salience probabilities. The final step of the static game analysis is to allow the outcomes to vary, and evaluate the consequences for the equilibrium.
The first proposition is derived from allowing the probability of high salience to vary in the preliminary game (as defined by the initial outcome values). In this case the proposition can be proven analytically in the specific context, but must be evaluated in the context of other payoff structures.
PROPOSITION 1: Increasing (decreasing) the probability of high salience increases (decreases) the likelihood of a negotiated settlement.
This proposition is intuitively straightforward. When the salience of the conflict is relatively high, the outcome is favourable to the intervener since the combatant will believe that any resistance is more likely to be defeated. Similarly, when salience is very low, combatants realize that the chance of having an intervener overpower any resistance is unlikely.
The initial assignment of outcomes, however, reveals more information. When the probabilities of high salience were allowed to approach either limit (1 or 0), then pure strategy Nash equilibria emerged. In fact, as soon as p > 0.5 in the initial game, 3 pure strategy Nash equilibria emerge, all leading to a negotiated settlement. Two of the three equilibria involved having the intervener always choose a weak intervention force regardless of the conflict's salience, while the third involved the intervener always choosing a strong intervention.<14> As soon as the probability of high salience falls below 0.5, there were no pure strategy Nash equilibria until p = 0, at which point the combatant always resists.
For cases where the probability of a conflict being regarded as high salience to the intervener is 0 < p < 0.5, any equilibrium in the initial game is the outcome of behavioral strategies.<15> The behavioral strategy in the first static game has the intervener always sending in a strong force when the conflict is of high salience. When the conflict is less important, the intervener will sometimes play strong, and sometimes play weak. In this case, the combatant will always resist a weak intervener, but will occasionally negotiate with a strong intervener.
Changing the probability of high salience (p) within the range of behavioral equilibria has effects which can be characterized in the following proposition:
PROPOSITION 2: In the range of solutions for which there is no pure strategy Nash equilibrium (0 < p < 0.5), an increase in the value of p leads to an increase in the probability that the intervener will use a strong force in a low salient game.
The intuition behind the proposition is somewhat more complex than in the previous case. When the probability of high salience is zero, the ethnic group will always challenge the intervener. Knowing this, the intervener seeks to minimize its intervention costs by minimizing its intervention i.e. it will always choose the weak intervention form. As the probability of high salience increases, the combatant will know that resistance will have a higher chance of leading its worst outcome. Thus it chooses to negotiate more frequently than in a situation in which the salience is likely to be lower. Under these conditions the intervener will select a random strategy which includes more strong interventions in an attempt to persuade the combatant of its commitment.
Solving the general game form for the behavioral equilibrium also provides insight into the role of the payoff structure. Thus, for the restricted domain of outcomes and probabilities for which a behavioral equilibrium occurs in the game, the following proposition can be made:
PROPOSITION 3: As the combatant's benefits of winning a challenge increase relative to the benefits from a negotiated settlement, the less likely the intervener will choose a strong intervention in a low salient conflict.
COROLLARY: As the combatant's benefits of a negotiated settlement increase relative to the benefits of losing a challenge, the more likely the intervener will choose a strong intervention in a low salient conflict.
The intuition behind Proposition 3 and its corollary is again very clear. With higher potential gains from successfully resisting an intervention, or the lower the potential losses from losing a challenge, the more likely the combatant will choose to resist. If the probability of resistance is high, then there is less incentive for the intervener to absorb the costs of a strong intervention.
Thus the basic structure of the game yields intuitively appealing results. The game can be modified in several ways to produce different types of equilibria. Specifically, four types of general equilibria can be produced: the intervener can play a pure strategy in high salient conflicts and a mixed strategy in low salient conflicts, a pure strategy in a low salient conflict and a mixed strategy for high salient conflicts, a pure strategy in both types of conflict, or a mixed strategy in both types of conflict. When the intervener plays a mixed strategy, the combatant must also be playing a mixed strategy, and similarly a pure strategy by the intervener will induce a pure strategy response from the combatant.
The difficulty with analyzing the game from the perspective of Nash equilibria is, as Binmore (1992) clearly indicates, the game requires each side to be able to derive their opponents strategy. Thus, actual observed outcomes may vary considerably depending on each side's beliefs about their opponent, beliefs which may or may not be accurate representations of true payoff structures or probabilities. The game's insight and formalization are still extremely valuable, however, for two reasons. First of all, repeated interactions allow players to learn about their opponents, as described in the next section. Secondly, rational players will still inform their strategy choice with their beliefs in order to derive `best' strategies under uncertainty. As the previous propositions illustrate, the formal game structure can identify how these strategies will vary according to different information sets.
Since the solution concepts considered thus far are Nash equilibria, there is already an implicit element of `learning' and `evolution' embedded in the model. In the next section, however, we consider how the static game would be transformed in a repeated framework.
5. Third Party Intervention under Uncertainty: A Dynamic Model
The static game is intuitive and versatile. In analyzing the game in a dynamic context, it can be interpreted as one of a series of interactions within a single conflict, or as a complete intervention in a sequence of separate conflicts. The analytical difference between these two frameworks arises in how the learning process occurs.
(a) Dynamics within a single conflict
Within a single conflict, the intervener will learn about the combatant and the combatant will learn about the intervener. Each party, in a sense, will be able to acquire information about the other's payoffs and, therefore, strategies. Within this context the notion of the Nash equilibria described in the previous section makes more sense, since Nash equilibria under uncertainty can be best thought of as an iterative process.
With imperfect information and a `Bayesian'- type learning process, the actual outcomes of a repeated game will take on interesting dynamic characteristics. Consider a high-salience contest (defined here as a single interaction out of a sequence of interactions between an intervener and a combatant within a single conflict) in which the players' a priori belief about the probability of the contest being salient is p = 0.4. The original game solution required the intervener to send in a strong intervention force. But because the intervener may also send in a strong force into a low salience contest, the combatant's best strategy is to occasionally resist a strong intervener. This mixed strategy leads to a probabilistic outcome: in the specific game, the combatant resists a strong force once out of every seven confrontations.
One random occurrence, presumably one which would occur more frequently, is for the combatant to agree to negotiate with the intervener and settle that round of the conflict peacefully. Doing so yields no information to the combatant regarding the actual level of salience, and hence they have no reason to adjust their perception of probability of salience, i.e. their evaluation of the probability p remains unchanged.
The second possible - though less likely - outcome is for the combatant to challenge the intervener. In this case the intervener will overpower the combatant and impose its desired settlement with respect to the issue at stake. In this case the combatant learns clearly that the contest, and perhaps the conflict as a whole, is salient to the intervener, and its revised optimal strategy is to simply negotiate on all future issues. In this case a pure strategy of negotiation by the combatant would also induce the intervener to reduce the costs of intervention by committing fewer troops.
Similarly, if the combatant challenges once in a non-salient contest, it will learn of the intervener's true absence of commitment and therefore adopt an aggressive strategy in all circumstances. Once again the optimal response would be for the intervener to reduce its commitment of forces.
These conclusions are useful in emphasizing why combatants will frequently choose to challenge interveners at some point in a conflict. Other aspects of these two portraits are clearly inaccurate, however. If salience becomes known, then indeed the outcome of the game becomes deterministic and both sides will follow the strategy which yields that solution at the lowest cost. Thus there are two additional complications that need to be considered.
First of all, the salience of any particular issue in a sequence of interactions could be partially independent of one another. Thus, discovering salience in one issue area may only give you partial information on salience on another issue. Subsequent strategy choices, and hence outcomes, may use beliefs about probabilities and payoffs which are only modified a little from original perceptions, and which reflect the retention of some uncertainty.
Secondly, and more importantly, the prospect of repeated interactions means that players now have an incentive to disguise their true preferences. Specifically, a weak intervener may choose to increase the strength of their forces in the face of a challenge even in a low-salience contest. By pretending to be committed early on, the intervener may deceive the combatant into believing that the conflict is of high salience and, therefore, that resistance in subsequent encounters is futile. Knowing that the intervener has this incentive, of course, makes the combatant more likely to challenge a well equipped intervention force. This process would then be evaluated through successive rounds of escalation (or negotiation).
How can the dynamic game be evaluated in light of several potential interactions and iterations? Two elements are crucial in terms of determining the eventual outcome: reputation of the intervener, and chance. A reputation for being tough in the face of resistance will lead combatants to evaluate the probability of high salience as being more likely, and would in turn make negotiations a more likely outcome. Similarly, if an intervener has a reputation for backing down then the probability of resistance will increase.
The benefits of a tough reputation are clear in terms of ability to win future contests at minimal cost. The magnitude of these benefits will depend on expectations about how frequently the contests will arise in the future. Not only will these expectations reflect the specific circumstances of a conflict situation, but they will reflect the intervener's beliefs about the attitude of the combatants. For example combatants which are risk averse will be less likely to challenge an intervener if the latter's response is not known.
There are costs of acquiring reputation however, and determining the `best' level of reputation must take these into account as well. Acquiring reputation will often entail using strong forces, and overcoming challenges by combatants, even in contests of little interest to the intervener. If these costs become too burdensome, then the investment in reputation will be correspondingly low.
What determines whether these costs become too high? The second crucial feature of the problem, and the one highlighted by the game structure, is the role of probabilities. Under uncertainty, outcomes are probabilistic. An `unlucky' outcome for an intervener will raise the costs of acquiring reputation by raising the likelihood of being resisted. Thus the game structure suggests that there is a degree of path dependence in the course of an intervention which may have a strong influence on the outcome. A series of poor outcomes at the beginning of an intervention may doom it to failure if the intervener then perceives that it will be challenged on every issue that arises in the future. Consequently the intervener may conclude that large investments in reacquiring its reputation will simply be too expensive, and it will abandon the effort.
(b) Dynamics between conflicts
The previous discussion applies largely unchanged to the context of sequential independent conflicts. The key differences with the previous case is that interveners will be less able to translate lessons about combatants from earlier conflicts into a new theatre, and combatants may reasonably expect the salience of consecutive conflicts to be more independent between theatres than within them. The issues of reputation and probabilities still arise in the case of successive conflicts. Path dependence is again likely to arise. When an intervention force fails in one conflict, possibly due to unfavourable random events, then the logic of game theory suggests that the intervener is more likely to be challenged elsewhere.
A more formal evolutionary game theoretic approach to the question is to use the "replicator approach". In traditional replicator games, each member of a population is imbued with a specific character trait that determines its behaviour in interactions with other members. The result (payoff) of an interaction is a function of these characteristics of the players, and in turn determine the relative probabilities of survival or "replication".
In the context of the model of third-party intervention, the standard approach must be modified to incorporate the fact that the crucial interaction is between two different "populations", i.e. interveners and belligerents. For example, consider the following simple model which focuses on the traits of the belligerents in a conflict. These belligerents are predisposed to either challenge or defer to a third party. As before, the third party's reaction depends on the salience of the conflict. The story underlying the replicator model can be told in terms of how successful the leader of a belligerent group is in managing the conflict. A leader that successfully challenges a third party intervener encourages other potential leaders to emerge which also have a predisposition to challenge. When a challenge leads to defeat by a third party (i.e. in conflicts of high salience to the intervener), the tendency to challenge becomes less appealing. Leaders who tend to defer to the third party attract some conciliatory members into the pool of potential leaders regardless of the conflict's salience to the intervener, but the attraction is less than that exercised by successful challengers.
Formally, the number of conciliatory potential leaders present after the end of a period of repeated interactions is N(1-p)(1+D?), where N is the total number of leaders present at the beginning of the period (assumed to be constant throughout the game), p is the proportion of confrontational leaders in the initial pool, D is the "coefficient of attraction" conciliatory leaders exercise over potential leaders, and ? is the length of the time period under consideration. The equivalent function for the confrontational leaders is Np(1 + qL? + (1-q)W?), where q is the proportion of high salient conflicts and L and W are "coefficients of attraction" associated respectively with losing or winning a challenge to an intervener. The ratio of confrontational-to-conciliatory leaders who actually emerge to lead the N belligerent groups is assumed to be equal to their proportion in the potential leadership pool.
These two equation can be substituted into the standard "replicator equation" (for details, see Binmore 1992, p. 418-419). It is straightforward to show that in this simple case the dynamic equation governing the change in the proportion of confrontational leaders over time is:
dp/dt = p(1-p)(qL + (1-q)W - D).
Two extreme cases can be dealt with immediately, as they emerge as a consequence of the game's simplicity. If p = 0 (i.e. no confrontational leaders) or p = 1 (i.e. no conciliatory leaders) there is no subsequent change in the proportion and the game is "at rest". This result is a common feature of standard replicator games because of the traditional emphasis on "genetic" replication; if a behavioral tendency is not present it cannot be replicated or, in this game's structure, emulated. Such a structure could be modified, however, to yield different results.
The key difference between this game and the standard replicator game is that the success of a strategy is dependent on the external environment rather than on the proportion of each characteristic in the leadership pool. Specifically, the probability of high salience conflicts (q) determines the other rest point, as does the relative values of D, L, and W. For example, when L = 0, D = 1, and W = 2, it is easy to see from the previous differential equation that an interior rest point will always occur if q = 0.5 regardless of the value of p, i.e. any proportion of conciliators-to-challengers could be an equilibrium if q = 0.5. For q < .5, dp/dt > 0 and the proportion of confrontational leaders would continuously increase until conciliators became extinct. For q > 0.5, it is confrontational leaders who would gradually disappear. The salience of the conflict in this model clearly becomes a key determinant of stability.
Although highly stylized, the results of this simple replicator model have some empirical potential. In a world in which all conflicts are salient, aggressive leaders would consistently lose challenges to powerful third parties, making that character trait less useful. With relatively passive belligerents, interveners could deploy minimal resources in the expectation of negotiated settlements. This equilibrium may be relevant to the Cold War era in reference to internal ethnic conflicts.
Of course, as the probability of high salience declines, aggressive combatants will begin to do better than their passive counterparts. While a balanced mix of passive and aggressive leaders may emerge, so might an equilibrium in which there are only confrontational leaders. Negotiation will disappear as a tactic and interventions will all be weak or, in the extreme, will not occur at all (i.e. the weakest form of intervention). It is arguable that in the post-Cold War world, more aggressive leaders have indeed increased in number in conjunction with what is arguably a decline in the salience of most conflicts to potential interveners. Evolutionary game theory, therefore, may have a contribution to make in explaining third party intervention, and may be useful in the evaluation of intervention strategies.
Conclusions and Policy Implications
As we approach the new millennium, questions of conflict management are becoming more and more central in a more decentralized global village. The destruction of national identities, whether through "ethnic cleansing" or less dramatic means, stands in the way of acquiring shared values that could provide a basis for inter-group cooperation (see Tcacik this volume).
What is the precise role for third parties in cases where a state fails or is weakened because political participation and opportunities become defined along narrow bands of ethnic sensibility? In a perfect world the best strategy would be to prevent ethnic tensions from leading to violence in the first place. However, on occasion it may be necessary for international forces to intervene directly in an ethnic conflict as peace enforcers. On occasion, the early and judicious use of force may be necessary, while impartiality may be both impossible and undesirable.
Recent events in Bosnia have demonstrated that the military and command requirements for conventional missions are distinct from those required to quell ethnic conflicts (see Harvey this volume). This paper has provided theoretical support for that argument. It is valuable to consider more closely what the evolutionary model of third party intervention means for the real world management of ethnic conflict.
The first observation is quite straightforward. At key turning points in the structure of global relations, state and sub-state actors are likely to face greater uncertainty regarding the motivations and capabilities of others and hence greater opportunities for conflict. At these crucial junctures, establishing reputations are crucial determinants of subsequent behavioral patterns. Acquiring a `good' reputation may also be less expensive in terms of resource commitments. In Bayesian terms, agents will have weaker prior beliefs and will therefore be more likely to consider initial behaviour as a strong signal of inherent characteristics. Positive signals early on, therefore, may have important benefits later on.
In this respect third party intervention in ethnic conflicts has not started off particularly well, as noted above. By failing to ensure that initial interventions were overwhelmingly successful, interveners may well have crippled their long term capability to intervene successfully by encouraging combatants to adopt more aggressive strategies. Overcoming the burden of this initial poor reputation will prove very costly in the future. The lack of determination displayed in the early rounds of the Bosnian crisis, as well as the eventual failure and force withdrawals associated with missions to Somalia and Rwanda, will have serious consequences for future missions.
Two further lessons which may be drawn from the analysis are relevant to the choice and structure of future interventions. First of all, having acquired a reputation for relative `weakness', interveners may find it useful to avoid areas of low salience and concentrate resources on conflicts which it is determined to win. By avoiding circumstances in which it is unlikely to stand up to a challenge, interveners will at least avoid sending any more embarrassing signals of weakness, while simultaneously conserving limited resources.
Secondly, the structure of intervention may also be worth examining. If the command structure, and its reliance on a coalition of forces (with obvious implications for free-riding incentives) has been a factor contributing to failure of U.N. missions, then U.N. interventions need to be reconsidered. Either their structure must change, or the U.N. should refrain from leading interventions, at least temporarily, until some means can be found to restore its reputation.
In the event that ethnic divisions are so horrific and destructive, should the international community consider incentives for the "breakup" of states based on mutual gain for the state-center and the minority? Such views are utopian at best and destructive at worst. Although peaceful secession can happen, the conditions are difficult to obtain even under the best of scenarios. Violent ethnic conflicts will continue to persist into the 21st century. There will be a continuing need for third parties to channel destructive ethnic conflict. Unfortunately, the governments and citizens of those countries which are likely to intervene in ethnic conflicts are also likely to question the value of investing in a reputation for committed intervention. With the consequent sub-optimal investment in reputation, interventions will become increasingly costly and, therefore, less likely. In this case the costs of ethnic conflict will fall not just overwhelmingly, but exclusively, on the average citizens in `unimportant' regions of the world.
1. The authors would like to thank the participants of the conference "Evolutionary Theory and its Critics" held at Utah State University in April of 1997, especially our discussant Veronica Ward and the conference co-chairs, David Goetze and Patrick James.
2. For example, Ward and Luterbacher's (1985) analysis of game theory considers a number of aspects of the dynamic behaviour crucial to any study of ethnic conflict. They are: a) each side's time preference, b) showing how different values attach to future versus present outcomes can lead to different decisions, c) the interactive play of crisis tactics, and d) the need to specify how actors can change their actions and when they will want to change their actions. Similarly Maoz's approach incorporates several dynamic factors. They are: measures of risk disposition into the expected utility calculations; measures of combat-related costs; and measures of intangible (moral and diplomatic) costs associated with aggression.
3. Weibull (1996) is one of many texts to which the reader can refer for greater detail.
4. Weibull (1996) indicates that the concepts of evolutionary stability can be apply directly to finitely repeated games.
5. A strategy's performance is determined not just by its scores against other strategies but also by the proportions of those strategies currently in the population. This process is conducted until the population dynamics stabilize (Signorino 1994).
6. According to Signorino (1996) the process continues until the territory converges to a steady-state population.
7. See Binmore (1992) for a description of the original Krep's game.
8. Specifically, Carment and Rowlands (1996) construct a game in which the key determinants are the salience of the conflict to the intervenor, the strength of the intervention, the strength of the ascendant combatant, and the expected gains to the combatant of pursuing the conflict. The game illustrates how these features affect the likely success or failure of intervention in a non-repeated game.
9. This assumption may be regarded by some as being highly objectionable. What must be kept in mind, however, is that the game structure is implicitly standardizing conflicts in terms of magnitude. Therefore, in terms of interpreting the model, it is not only salience which matters, but salience relative to the amount of resources necessary to subdue the combatants. Thus Rwanda may be viewed as an unimportant conflict by some states, but the resource costs of intervening may similarly be quite low. While it may be possible to rank conflicts according to their salience, ranking them according to how intervenors regard the salience-to-resource requirement tradeoff will be considerably more difficult. It is this more difficult ranking which the game is treating as essentially random.
10. It should be noted that the evaluation of the size of the intervention force must be made relative to the combatants. What constitutes a small intervention force in one conflict, eg. Bosnia, may represent a powerful intervention in another conflict, eg. Rwanda.
11. Carment and Rowlands (1996) include a further round of interaction (the intervenor can withdraw or resist a challenge), and allow chance to determine the outcome of any confrontation. To keep this game as simple as possible, Kreps' approach is used in which probabilities determine the players' characteristics, but the outcomes of strategic choices are deterministic.
12. The assumption that the intervener possesses superior resources could be modified, and the outcome of a challenge made probabilistic. Recent history, however, suggests that most interventions of the type we are considering involve the United Nations generally, and the United States specifically, as the intervener. Thus the assumption seems justified.
13. Intervention has economic as well as military traits, and therefore we do not restrict ourselves to military intervention as a bargaining strategy. Military intervention does not preclude economic measures. However, the benefits of applying these restrictions to multilateral interventions are two fold. First it allows us to separate out military strategies that are appropriate under a given set of conditions that include low and high salience for the mission. This assumption is consistent with current policy perspectives on third party intervention in intrastate conflicts which call for measures that lay somewhere between peacekeeping and peace enforcement
14. At the extreme of p = 1, the game collapses into a two-by-two strategic form with two Nash equilibria. In the game, however, the eventual solution will actually be for the intervener to send in a weak force and the combatant to negotiate, since the combatant's weakly dominant strategy is always to negotiate.
15. See Binmore (1992) for a discussion and example.
16. Robert Young "How Do Peaceful Secessions Happen?" in Carment, D. and James P. eds. Wars in the Midst of Peace (Pittsburgh, University of Pittsburgh Press, 1997). Citing evidence that includes Norway's secession from Sweden, the breakup of Czechoslovakia and Singapore's departure from the Malaysian federation, among others, Young argues that peaceful secession conditions include major third party involvement and an implementation and negotiation process that is almost entirely elite led. The process must also be swift.
Axelrod, R. The Evolution of Cooperation (Michigan University Press, 1984).
Binmore, Ken (1992): Fun and Games: A Text on Game Theory (Lexington: D.C. Heath and Company).
Brams, S. and M. Hessel (1984): "Threat Power in Sequential Games," International Studies Quarterly 25: 242-254.
Brecher, M. (1994): Crises in World Politics (Toronto: University of Toronto press and Pergamon).
Brecher, M.and P. James (1989) Conflict Crisis and Instability (Oxford: Pergamon Press).
Brecher, M. (1984) Crisis and Change in World Politics (Boulder: Westview Press, 1986).
Bueno de Mesquita, B. (1981) The War Trap (New Haven, CT: Yale University Press).
Carment, David, and Dane Rowlands (1996): "Explaining Multilateral Intervention in Ethnic Conflict: A Game Theoretic Approach," Npsia Working Paper Series.
Dixon, W.J. (1996): "Third Party Techniques for Preventing Conflict escalation and Promoting Peaceful Settlement," International Organization 50:4.
Fearon, James (1995): "Rational Explanations of War," International Organization 49(3): 379-414.
Kriesberg, Louis (1997): "The Phases of Destructive Communal Conflicts" in D. Carment and P. James, eds. The International Politics of Ethnic Conflict (Columbia: USC Press).
Lake, David and Donald Rothchild (1995)" "Ethnic Fears and Global Engagement: The International Spread and Management of Ethnic Conflict". San Diego: IGCC Working Paper.
Lund, M.S. (1996): Preventing Violent Conflict: A Strategy for Preventive Diplomacy (Washington D.C.: United States Institute of Peace Press).
Morrow, J. "Game Theory and Conflict" in Ward, D. and U. Luterbacher, eds. (1985): Dynamic Models of International Conflict (Boulder: Reinner Press).
Maoz, Zeev (1990): National Choices and International Processes (Cambridge: Cambridge Press).
Ruggie, J. (1994): "The New U.S. Peacekeeping Doctrine", The Washington Quarterly 17(4).
Ruggie, J. (1993): "Wandering in the Void: Charting the UN's New Strategic Role" Foreign Affairs (Nov/Dec.): 26-31.
Signorino, Curtis (1996): "Simulating International Cooperation under Uncertainty," Journal of Conflict Resolution 40(1):152-205.
Wallensteen, Peter and Margareta Sollenberg, (1995) "After the Cold War: Emerging Patterns of Armed Conflict 1989-94", Journal of Peace Research 32: 345-360.
Ward, D. and U. Luterbacher, eds. (1985): Dynamic Models of International Conflict (Boulder: Reinner Press).
Weibull, Jurgen (1996): Evolutionary Game Theory (Cambridge, Mass.: MIT Press).
Young, Robert (1997): "How do peaceful Secessions Happen?" in D. Carment and P. James, eds. Wars in the Midst of Peace (Pittsburgh: University of Pittsburgh).
Zartman, W. (1989): "Alternative Attempts at Crisis Management: Concepts and Process," in G. Winham, ed. New Issues in International Crisis Management (Boulder: Westview Press).
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