Human Rights

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Is Enforcement Necessary for Effectiveness? A Model of the International Criminal Regime Author(s): Michael J. Gilligan Source: International Organization, Vol. 60, No. 4 (Autumn, 2006), pp. 935-967 Published by: Cambridge University Press on behalf of the International Organization Foundation Stable URL: http://www.jstor.org/stable/3877852 Accessed: 01-11-2016 19:17 UTC

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Is Enforcement Necessary for Effectiveness? A Model of the

International Criminal Regime Michael J. Gilligan

Abstract Recently, scholars have questioned whether enforcement mechanisms are necessary to make regimes effective. This article provides a model of the inter- national criminal regime in which the regime changes state behavior even though it possesses no enforcement mechanisms. The article also answers several prominent criticisms of the International Criminal Court (ICC). Critics claim that the ICC is at best futile because it lacks the power to apprehend the criminals it is meant to prosecute. Even worse, the ICC may be harmful because it will induce atrocious leaders to hold on to power longer than they would if they could step down with immunity for past crimes. The model in this article suggests those criticisms may be inaccurate. I model the interaction between a leader and a foreign state that has the option of offering that leader asylum. I examine the effect of the creation of an ICC-like institution on that interaction. The model produces three main findings. (1) Leaders' reigns will not be prolonged as a result of the regime. (2) Although the institution has no enforcement power, some leaders (those with such a high proba- bility of being deposed that they would willingly surrender to the institution rather than try to stay in office) will be punished by it. In those circumstances, the foreign state has no incentive to offer the leader asylum. (3) The institution may deter some atrocities at the margin.

In February 1979, Idi Amin, one of the world's most notorious dictators, escaped Uganda, the chaotic country he had led for almost two decades. Some 300,000 people are believed to have died as a result of Amin's reign. Ultimately Amin died in Saudi Arabia in August 2003, never having answered for his crimes. Milton Obote, Amin's successor (who, ironically, Amin had forced into exile eighteen

I would like to thank Tanaz Moghadam, whose undergraduate honors thesis, which William Clark and I advised, provides an earlier game-theoretic analysis of the Court and introduced me to the topic of the ICC. Special thanks go to William Clark for the idea of treating the ICC game-theoretically and for valuable comments at various stages of this project. I am grateful to Lisa Martin and two anony- mous reviewers who provided exceptionally helpful insights. I would also like to acknowledge Sandy Gordon, Dimitri Landa, James Morrow, Steve Ratner, Shanker Satyanath and Ken Scheve for their much-appreciated input. All errors remain my responsibility.

International Organization 60, Fall 2006, pp. 935-967 ? 2006 by The IO Foundation. DOI: 10.1017/S0020818306060310

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936 International Organization

years earlier), was by some accounts guilty of torturing and killing even more people than Amin. Toppled in a coup in 1985, Obote obtained asylum in Zambia, where he died in October 2005 seeking hospital treatment in South Africa.' Cases such as Amin's and Obote's are unfortunately not uncommon. Other examples include Jean-Claude "Baby Doc" Duvalier, who is accused of torture and political assassinations in Haiti and who lives comfortably in France. Ferdinand Marcos, the extraordinarily corrupt dictator of the Philippines, lived out his days without punishment in Hawaii. The list could go on.2

Such cases are disturbing for at least two reasons. First, there is the obvious normative concern that perpetrators of atrocities are not being punished for their crimes. Second, there is the more practical question of deterrence-if leaders who commit atrocities are able to get off scot-free, what hope is there of deterring such crimes in the future? In part to help prevent the recurrence of cases such as those described above, a group of states created the International Criminal Court (ICC) in 1998 after a half-century of on-again-off-again negotiations. The ICC entered into force in summer 2002, and in summer 2003 the Court's first Chief Prosecu- tor, Luis Moreno-Ocampo, was appointed.3

While the modal opinion in legal journals probably supports the creation of the ICC, the Court has been the object of virulent criticism from both legal schol- ars and policymakers. Unfortunately neither the Court's proponents nor its detrac- tors have been particularly rigorous in how they have made their arguments, so it is difficult to tell if the disagreement stems from faulty logic or simply from differences in unstated assumptions. This article attempts to contribute to the debate by offering a more formal argument about the possible implications of the cre- ation of the ICC. I focus on two criticisms of the Court: (1) the ICC will fail to be effective because it lacks enforcement, and (2) the ICC will prolong the reign of leaders who have abused human rights and make it more costly to get rid of them.

Goldsmith offers a forceful example of the first critique:

[T]he ICC is unlikely to punish the Husseins and future Milosevids of the world because it is unlikely to get a grip on them. The ICC has no inherent enforcement powers. It depends completely on member states to arrest and transfer defendants. So the efficacy of... prosecutions depends on the uncer- tain resolve of nations to use military or economic force to extricate the oppres- sive leader from his country.4

1. See "Obituary: The Buffoon Tyrant," BBC News, 16 August 2003; and "Obituary: Milton Obote," BBC News, 18 October 2005. Available at http://news.bbc.co.UK/2/hl/africa/597725.stm. Accessed 26 March 2006.

2. "No One Writes to the Tyrants," Guardian Unlimited, 20 January 2003. Available at (http:// www.guardian.co.uk/Iraq/Story/0,2763,878739,00.html). Accessed 26 March 2006.

3. Information on current events at the ICC is available at (http://www.icc-cpi.int/otp/ otp_events.html).

4. Goldsmith 2003, 92. See Smidt 2001 for the same argument.

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International Criminal Regime 937

If this argument is correct, then by implication the ICC cannot be expected to fulfill the goal of deterring atrocities.5 Krasner provides a particularly nice exam- ple of the second criticism:

Baby Doc Duvalier ... ended up living on the French Riviera.... Idi Amin, ... has lived in Saudi Arabia for the last twenty years now.... [W]hen you think about justice and especially Idi Amin, who killed a lot of people, the ques- tion is this: was it better to offer him sanctuary in Saudi Arabia, or would it have been better to say to him when he was still in power, "We are going to prosecute you?" The reaction of any autocratic ruler under those circumstances would be to hold on to power as long as he possibly can.... Threatening these actors with prosecution may make it more difficult to get rid of them.6

I analyze these criticisms within the context of a game-theoretic model. I show that despite the lack of an international police force to enforce its indictments, the ICC may still deter leaders from committing atrocities at the margin because it offers potential asylum-granting states the option of refraining from offering asy- lum to atrocious leaders who are so likely to be deposed that they would willingly surrender to the ICC to avoid retribution from domestic political rivals (which I assume is worse than the punishment handed out by the Court). Since all leaders know that there is some chance (however remote) they will be in that position, the expected present value of committing atrocities is reduced, and at the margin some leaders will refrain from committing them.

The model also suggests that the concern that the ICC will prolong tyrants' reigns may be exaggerated. The ICC, as with any international institution, must be self-enforcing. States will only comply with it if they have the incentive to do so. The ICC has no power to punish states that harbor atrocity committers, so states will refrain from doing so only when it provides at least as high a payoff as not doing so. In this model they will only refrain from offering such leaders asylum when those leaders are so likely to be deposed that they are willing to surrender to the ICC, and therefore the reign of atrocity-committing dictators will not be pro- longed as a result of the creation of the institution.

A second contribution of this article concerns the role of enforcement in mak-

ing international regimes effective. International relations scholars have known for some time that "trigger strategies" can induce states to comply with inter- national regimes despite their lack of a higher authority to enforce those rules as long as the states' interactions are repeated indefinitely and they do not discount future payoffs too heavily. According to other literatures, these enforcement pro- visions are unnecessary for regimes to be effective. Compliance is either simply a

5. For a focus on the ICC's capacities (or lack thereof) to deter atrocities, see Wippman 2000; and Smidt 2001. For a more positive assessment, see Akhavam 2001.

6. Krasner 2003. The same argument can be found in Goldsmith 2003 and Goldsmith and Krasner 2003.

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938 International Organization

management problem or enforcement is unnecessary because norms or new knowl- edge created by the regime induce states to comply with its rules.

This article offers a rational choice model of an international institution that

alters states' behavior even though it is not enforced by trigger strategies or any other mechanism. Furthermore, the model does not resort to "epistemic commu- nity" or norms arguments, nor does it treat noncompliance as a management prob- lem. There is no outside intervention either by states or international organizations to depose leaders who commit atrocities, and states that harbor such leaders are not punished in any way. Still, states may refrain from offering asylum when the dictator's hold on power is sufficiently tenuous because they know the dictator would be willing to surrender to the ICC. States only comply with the institution's indictments when it is costless to do so. They will regularly fail to comply with the regime modeled here, by which I mean they will continue to grant asylum to leaders who have committed atrocities; however they will comply with it enough to deter atrocities at the margin.

In short, the article contributes to both the policy debate surrounding the ICC and the theoretical literature on enforcement and international cooperation. While the model offers no hope that the creation of the ICC will bring about a world free of atrocities, it does offer a set of conditions under which there will be marginally fewer atrocities thanks to the creation of the institution. Furthermore, there is no

downside to creating the institution in this model since the reign of atrocity- committing leaders is not prolonged as a result. Second, the model offers an inter- esting example of a rational choice model in which an international institution is effective even though no punishments (whether tit-for-tat, grim trigger, and so on) are employed to enforce compliance.

In the next section I review the debate on the necessity of enforcement for regime effectiveness and discuss the implications of the model for that debate. In the sec- ond section I turn to a discussion of the literature on the ICC. The third section

offers an informal discussion of the model and its results. I highlight a few fea- tures and extensions of the model in the fourth section before concluding in the final section.

Is Enforcement Necessary for Regimes to Be Effective?

The main implication of this research for broader international relations theory con- cerns enforcement and the efficacy of international regimes.7 The cooperation prob- lem modeled here shares a variety of features that are common to international institutions more generally-the lack of a police force, reliance on sovereign states,

7. I would like to thank the editor and the two anonymous reviewers for pointing out this contribu- tion of the model.

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International Criminal Regime 939

and nonuniversal membership. One of the main endeavors of international rela- tions scholarship over the past two decades has been to answer the question of how international agreements can have any effect on state behavior under such circumstances.8

The game-theoretic approach provides one answer via the "folk theorem." If the interaction between states is repeated indefinitely, states can enforce their treaty commitments by employing trigger strategies. Cooperation is enforced by the cred- ible threats (either implicit or explicit) of the other members of the agreement to revert to noncooperation for some subsequent amount of time in punishment for any deviation from cooperation. Even in cases where noncompliance is a domi- nant strategy in the one-shot interaction, states will comply with their commit- ments. According to these theories, states would fail to comply with agreements and the agreements would have no effect on state behavior without such enforce- ment mechanisms.

More recently, scholars have questioned whether these types of enforcement mechanisms are the best way to understand states' compliance with their treaty commitments and whether they are necessary or even desirable for international agreements. One such group of scholars has been dubbed the "managerialists" by Downs and colleagues, who provide a nice summary of managerialist thinking:

Its message is that (1) compliance is generally quite good; (2) this high level of compliance has been achieved with little attention to enforcement; (3) those compliance problems that do exist are best addressed as management rather than enforcement problems; and (4) the management rather than the enforce- ment approach holds the key to future regulatory cooperation in the inter- national system.9

Downs and colleagues are quite critical of this argument. They question whether the relatively good record of compliance indicates that enforcement is unimpor- tant since in equilibrium, regimes will be designed to bring about compliance. One cannot infer from the sterling record of compliance whether enforcement mea- sures are unnecessary or very necessary but also very effective. Furthermore, if enforcement provisions are weak or nonexistent as managerialists contend, high rates of compliance are probably due to shallow treaties. They argue that we should not be sanguine about the combination, touted by managerialists, of weak or non- existent enforcement and high rates of compliance because that combination implies shallow treaties.10

8. This discussion is necessarily brief. For a fuller discussion, see Martin and Simmons 1998; Simmons 1998; Raustiala and Slaughter 2002; and Simmons and Martin 2002.

9. Downs, Rocke, and Barsoom 1996, 379. Examples of managerialist works include Chayes and Chayes 1993 and 1995; Haas, Keohane, and Levy 1993; Mitchell 1993 and 1994; and Young 1994.

10. Downs, Rocke, and Barsoom 1996. Also see Simmons 1998, 80, for a discussion of this debate. Tallberg 2002 takes the middle ground, arguing that within the European Union (EU) both approaches are used and both are valuable in promoting compliance.

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940 International Organization

Another school of thought that regards enforcement as unimportant for regime effectiveness is the normative approach (often associated with constructivism). According to this approach, credible punishments for noncompliance are not what change state behavior. Instead, regimes change states' preferences away from non- cooperation toward cooperation by establishing new norms that alter states' per- ceptions of what behaviors are acceptable." A third literature that considers enforcement unnecessary for regime efficacy points to "epistemic communities" and learning.12 According to this literature, communities of experts associated with the regime generate new knowledge about the benefits of international cooperation. Enforcement becomes unnecessary as states learn that cooperation is in their best interests. Finally, Dai offers a rational choice model in which states comply with their international commitments despite the absence of international enforcement mechanisms. In her model, states comply with their commitments because they are pressured to do so by powerful domestic constituencies that prefer compliance.13

Similar to the accounts described in the preceding paragraph, the regime mod- eled in this article has no enforcement provisions either explicit or tacit, and states are not punished for noncompliance. Unlike those accounts, neither norms nor learn- ing play any role in the model, nor does the model treat compliance as a simple management problem or rely on pressure from domestic constituencies. States in the model often will strictly prefer noncompliance (that is, offering asylum to indicted leaders) and will fail to comply in such situations. Indeed, contrary to the accounts described above, noncompliance will be quite frequent in this model, and yet it is still effective in that states comply with it enough that it does deter atroc- ities at the margin. The regime modeled here is crucial to this change in state behav- ior because without it, the foreign state would continue to offer asylum to dictators in those cases where it refrains from doing so after the creation of the regime.

Indeed, this discussion raises the issue of whether a good record of compliance is even necessary for regimes to be effective. The two concepts, compliance and effectiveness, are sometimes conflated in the literature. However, as Raustiala and Slaughter point out, "[R]egimes can be effective ... even if compliance is low. And while high levels of compliance can indicate high levels of effectiveness they can also indicate low, readily met and ineffective standards."'4 Downs, Rocke, and Barsoom are clearly concerned about the latter phenomena.'5 Depending on one's definition of "effectiveness", the model in this article provides a set of con- ditions that produce the former.16

11. Simmons 1998 offers a review of this literature. A few examples from the large norms literature include Kratochwil and Ruggie 1986; Franck 1990; Nadelman 1990; Klotz 1995; Florini 1996; Finnemore 1996; Legro 1997; Finnemore and Sikkink 1998; Keck and Sikkink 1998; Price 1998; Clark 2001; and Rudolph 2001.

12. See Haas 1989; and the articles in Haas 1992. 13. Dai 2005.

14. Raustiala and Slaughter 2002, 539. 15. Downs, Rocke, and Barsoom 1996. 16. See also Keohane, Haas, and Levy 1993; Young 1994; and Victor, Raustiala, and Skolnikoff 1998.

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International Criminal Regime 941

In summary, the model provides a rational choice account of a regime that changes state behavior but where enforcement is unnecessary and perhaps even undesirable because it may introduce commitment problems and prolong atro- cious leaders' reigns. Members of the regime frequently will fail to comply with the regime but they will occasionally comply, which is enough to deter atrocities in some cases. Harsher punishments for members who offer asylum to indicted leaders would induce more compliance but may come with the added cost of pro- longing the rule of atrocious dictators.

Previous Research on the ICC

The legal literature on the ICC is voluminous, so a thorough review of it is beyond the scope of this article. The political science literature on the topic is sparser, and can be divided into theoretical and empirical contributions. Turning first to the theoretical contributions, the only other game-theoretic treatment of the ICC of which I am aware is Moghadam, who argues that the ICC may deter atrocities." The source of this deterrent effect is an intervention to punish human rights abus- ers by "the international community." As such, her model fails to address the crit- icisms that such interventions are unlikely. Furthermore, it does not address whether the ICC will prolong the reign of leaders who have committed atrocities.

In a rational-choice-based case study of a related topic-treaties on treatment of prisoners of war-Morrow argues that states refrain from violating POW trea- ties in times of war because if they did, their enemies may retaliate by doing the same.'8 Thus the game has the characteristics of the classic repeated prisoners' dilemma. Morrow provides evidence of this process at work in Nazi treatment of prisoners of war (POWs) during World War II. Morrow's analysis highlights the particular difficulties inherent in an international criminal regime that is meant to deter atrocities committed by leaders against their citizens (as opposed to foreign combatants), because nothing like the same enforcement mechanism exists.

Meernik also raises some of the questions raised here: "To what extent should we expect the international community to hold individuals accountable? Will indi- vidual leaders comply with international law? Most importantly, what factors will influence the level of enforcement of and compliance with international law?"19 Rather than developing a theoretical model, however, Meernik's approach is to suggest covariates that will correlate with these behaviors. Meernik's answers are of course speculative because the ICC has yet to try anyone. He suggests inter alia that states that have shown a commitment to international law as indicated by their support for human rights treaties in the past, as well as democratic states, should be more supportive of the ICC ceteris paribus.

17. Moghadam 2004. 18. Morrow 2001.

19. Meernik 2004, 356.

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942 International Organization

Turning to empirical studies, Meernik and Shairick examine the kind of states that have acceded to the ICC and find that states with high degrees of civil liber- ties are more likely to do so. They also find that states with a greater dependence on foreign aid and more foreign debt are more likely to sign the Rome Statute. Meernik and Shairick interpret this latter finding as evidence that economically strong states with a commitment to the ICC have been able to use economic lever- age to induce smaller states to sign the treaty.20 Kelley examines the types of coun- tries that have entered into "Article 98" agreements with the United States.21 She finds that states that are relatively large, powerful, democratic, and that have strong norms of rule of law are less likely to sign such agreements.

Rudolph's paper was published before the Rome Statute entered into force, so his discussion is understandably highly qualified. Applying a constructivist norms- based approach to case studies of three ad hoc international criminal tribunals and the negotiations over the Rome Statute, he infers: "The evidence suggests that expanding liberal norms of state conduct and protecting human rights cer- tainly explain the existence of tribunals in locales with little strategic or material importance."22

In short, research on the ICC has been dominated by empirical studies, both qualitative and quantitative, on the negotiations of the Rome Statute and of the types of countries that have signed it and most closely adhered to the spirit of it by refraining from Article 98 agreements. Given the youth of the regime, it is understandable that none of this work offers much insight into the pros- pects for an effective ICC. What theoretical work there has been either assumes away the problem of enforcement by including an "international community" that intervenes to impose the Court's indictments or addresses war crimes trea- ties, which (as Morrow has convincingly argued) plausibly possess the self- enforcing features which are common in rational choice models of international cooperation but which are absent in the case of the ICC. Thus, this article con- tributes to the literature on the ICC by offering a model of the regime that explic- itly addresses its inherent lack of enforcement in a rational choice framework. I now turn to that model.

Informal Presentation of the Model and Results

In this section I will first provide a brief overview of the logic of the argument. I will then turn to a fuller discussion of the players and their preferences. Following

20. Meernik and Shairick 2005.

21. Kelley 2005. In these agreements, states pledge to refrain from surrendering each other's citi- zens to the ICC. The agreements are allowed under Article 98 of the Rome Statute (thus the name). The American Service Members' Protection Act of 2001 requires such agreements before member states of the ICC are eligible for U.S. military aid. As of this writing, the United States has concluded ninety- two of these agreements.

22. Rudolph 2001, 681.

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International Criminal Regime 943

that, I will discuss the timing of the model and then present the results in some- what more detail and offer some intuition and comparative statics for the results. The model is presented more formally in the appendix.

Logic of the Argument

The logic of the argument can be summarized as follows:23

1. Dictators' payoffs (in expected present value) of committing atrocities are increased if they can expect asylum when they have low odds of retaining power and they face domestic retribution that they could avoid by asylum.

2. Foreign countries prefer not to have atrocity-committing dictators in power in other countries and so cannot credibly commit to deny asylum to an asylum- seeking human rights abuser.

3. Voluntary surrender to the ICC is worse for human-rights-abusing dictators than asylum but may in some cases be better than attempting to stay in power because of the risk of retribution from their domestic political rivals (which I assume is worse than the punishment imposed by the ICC) if they are deposed.

4. The existence of the ICC allows foreign countries to credibly reject requests for asylum in these cases, because dictators will voluntarily step down peace- fully and surrender to the ICC.

5. Thus the existence of the ICC lowers the expected present value of commit- ting atrocities in the first place, because there is a chance dictators will find themselves in the position of preferring to surrender to the ICC, when with- out the ICC they would have obtained asylum in a foreign land in such a case. This is the ex ante deterrence effect.

6. Since states that are potential safe havens for dictators can ignore the ICC without penalty, the regime does not reduce their incentive to grant asylum except in cases where dictators prefer surrendering to the ICC than staying in power, and because surrendering to the ICC is completely voluntary, the option does not increase dictators' incentive to hold on to power to avoid ICC prosecution. Thus the regime does not increase dictators' incentive to cling to power to avoid prosecution.

In a nutshell, the existence of the regime modeled here allows states to credibly refuse asylum in some cases when, without it, they would prefer to offer it, and it does so without prolonging the reign of atrocity-committing dictators.

23. I thank an anonymous reviewer for this cogent summary of my argument.

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944 International Organization

Players and Their Preferences

There are three players in the model at any given time: the leader (Li, iE{1, 2, 3, ...}), the foreign state (S),24 and nature (N). Nature chooses new leaders as the old ones are deposed and also randomly chooses the probability that a leader who

has committed atrocities is deposed. I call this randomly drawn probability, at (the t subscript denotes the relevant period). For simplicity, the probability that leaders survive a given period if they do not commit atrocities is fixed throughout their reign. There is only one leader at any given iteration of the stage game. If leader Li is deposed in the previous period, Nature chooses the next leader, Li+j, at the start of the subsequent period. Leaders are indexed in the order they are chosen. The identity of the foreign state does not change at any point in the game. Leaders receive a payoff of I each period they are in power and a payoff of 0 each period they are not in power. If leaders are deposed having committed atrocities they suffer a one-time cost of -r. If they are deposed not having committed atroc- ities, they receive a one-time payoff dE(-r, 1). In other words, I assume that the costs after being deposed are strictly worse for a leader who has committed atroc- ities than for a leader who has never committed atrocities. Leaders care only about staying in power, which they strictly prefer to not being in power, and the punish- ment they suffer if deposed. The foreign state is assumed to strictly prefer a leader who has never committed atrocities. An important feature of the model is that there is no foreign intervention to depose leaders. Leaders are deposed only by domestic political rivals.

Timing of the Model

The extensive form of the game is presented in Figure 1. The timing in the model is as follows. A new leader (Li) is chosen by Nature (N). Nature then chooses the probability that that leader Li will be deposed if he or she commits atrocities and, knowing that probability, the leader chooses whether or not to commit atrocities. If leaders do not commit atrocities, they can request asylum abroad or they can take their chances on surviving in office. If they survive, the game repeats and a new survival probability is drawn. If however leaders commit atrocities, they face a lottery over their political survival. If leaders survive until the following period they enter the postatrocities subgame. In each iteration of that subgame a new at is drawn. Knowing that probability, leaders decide whether to request asylum or to take their chances on the lottery over their political survival. If the leaders request asylum, the foreign state has the choice of granting it or not granting it. If the foreign state refuses to grant asylum, leaders face a lottery over their survival as described above. Committing atrocities has an irreversible effect in that once lead- ers commit atrocities, their probability of survival is given by the random variable

24. The model generalizes straightforwardly to multiple foreign states.

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International Criminal Regime 945

1.N

Choose leader

2. N

draw a,

3. Li Atrocities o atrocities

Request4L asylum Do not request

Li deposed 5ylum Return to Reject Accept node 1

Li survives 7. N Return to 6. N node 1

Li survives Li deposed Return to Return to node 2 node 1 Li survives Li deposed

Return to Return to Postatrocities 9 N node 2 node 1 subgame

draw a,

10. Li

Request Do not asylum request

asylum

Reject Accept

12. N Return to node I

Li survives Li deposed Return to Return to Li survives Li deposed node 9 node 1 Return to Return to

node 9 node 1

FIGURE 1. Game form of the stage game, preinstitution

a, in each period thereafter, and if they are deposed, they suffer a retribution pun- ishment regardless of whether they commit atrocities in that period or not.

In short, leaders' decision of whether or not to commit atrocities is a trade-off

between the increase in their probability of surviving politically that committing

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946 International Organization

atrocities may afford versus the extra costs of the more severe punishment they will suffer if they are deposed. The possibility of asylum abroad mitigates this latter concern because the leaders know that if their probability of surviving in office becomes too low, they have the option of requesting asylum and (assuming that request is honored) going into exile with impunity.

Results

In this section I will describe the results in somewhat more detail and provide the intuition for them. Readers should turn to the Appendix for a complete explication of the model. First, I will describe the outcomes in the model before the inter- national court is created. I will then turn to the outcomes in the model after the creation of the international court to show the effects of the institution on the lead-

ers' incentive to commit atrocities and to show that leaders have no increased incen-

tives to hold on to office longer than they would without the institution.

Preinstitution. In the preinstitution setting the foreign state has a dominant strat- egy to accept the leader's request for asylum. The foreign state is assumed to suf- fer disutility from there being a leader in power who has committed atrocities. Once a leader commits atrocities, the foreign state would prefer that that leader be removed from power because there is some chance (depending on Nature's draw of a, 1) that the subsequent leader will not commit atrocities. Thus by accepting the current leader's request for asylum the foreign state will get rid of an atrocious dictator for sure. However, if the foreign state rejects the leader's request, it is rid of the current leader only with probability 1 - at.

The leader's equilibrium behavior is equally straightforward. Leaders will com- mit atrocities if doing so increases their probability of remaining in office by a sufficient degree. Leaders will not commit atrocities for a small increase in their probability of remaining in office, because once leaders commit atrocities they "cross the Rubicon" in the sense that they will have to pay the retribution costs for their past atrocities whether they continue to commit atrocities or not. Once leaders commit atrocities they will play the lottery over their political survival in subsequent periods as long as Nature draws a high enough probability that they will survive. If, however, Nature draws too low a probability, leaders will choose to request asylum. In such a case, their expected present value from exile with asylum is higher than from attempting to hold on to political office where there is a chance they may be deposed and have to pay the retribution cost. In fact there is a cutoff level of at, which I call a, for which leaders are indifferent between request-

ing asylum and playing the lottery over their survival. For values of at lower than a, the leader strictly prefers asylum in a foreign land to attempting to stay in office,

and as I already discussed, the foreign state has a dominant strategy to accept such a request. Therefore, in such a situation the leader will request asylum and it will be granted.

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International Criminal Regime 947

Leaders commit atrocities in this model when doing so increases their chances of surviving politically and when the penalty they suffer if they are deposed hav- ing committed atrocities (- r) is small relative to the payoff of being deposed not having committed atrocities (d). The italicized qualification is important because casual empiricism would suggest that the penalties from being deposed in states most plagued by atrocity-committing leaders are quite high and may include assas- sination or execution possibly preceded by torture. The point is that the penalties of being deposed not having committed atrocities are also quite high in these states, and may also involve torture and death. By comparison, being deposed in states not prone to atrocities is not that unpleasant. Financially lucrative book deals and speaking engagements are the norm; assassination and detention are quite rare.

Figure 2 illustrates this difference between two hypothetical states. In country 1 the norm for political succession is assassination. In country 2 the norm for polit- ical succession is well-ordered transfers of power with the loser going into august retirement. In other words, d is considerably higher in country 2. Assume that the retribution costs of being deposed having committed atrocities are the same in both states. As illustrated in Figure 2, the difference in the penalty of being deposed after committing atrocities compared to the penalty of being deposed after not committing atrocities is quite small in country 1. In country 2, by contrast, the difference between these two penalties is quite large. In both cases the penalty to the leader from committing atrocities is identical, but d is lower in country 1 because of the two different norms of succession. As such, the leader would have more incentive to commit atrocities in country 1 than in country 2.

Figure 3 illustrates the effect of increasing the retribution costs. Higher retribu- tion costs reduce leaders' expected present value of committing atrocities. As such, leaders' expected present value of committing such abuses will be lower for any

given value of at and leaders prefer asylum to attempting to stay in power for relatively higher values of at. Leaders will step down with higher probabilities of surviving in office and they are less likely to commit atrocities in the first place (that is, Nature must draw higher values of at before they are willing to commit atrocities).

Country 1

-r d 0 1

Country 2

-r 0 d 1

FIGURE 2. Differences in scale arising from different norms of succession in two different states

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948 International Organization

EPV

1 +6U'-------------------------------------- 1+U"................................

1 + 6U"

Li's EPV when r = r': at(1 + r' + 6U) - r'

Li's EPV when r = r": at(l + r" + bU") - r"

a + r'+8U

0 at 1

Range of possible agreements Range of no possible agreements when r = r" when r = r"

Range of possible i Range of no possible agreements when r = r' agreements when r = r'

Increase in range of possible agreements from increase

in retribution costs

Note: Larger retribution costs expand the range of leaders' probabilities of survival (at) for which there is a possible asylum agreement. Increasing retribution costs from r' to r" expands the range of at for which there are possible asylum agreements from zero to a' to zero to a".

FIGURE 3. Comparative statistics on a, and r

Postinstitution. The institution modeled in this article creates a nonstrategic actor, the prosecutor, who automatically indicts any leader who commits atrocities.25 If the foreign state becomes a member of the regime it pledges not to offer asylum

25. Obviously this assumption is not general. Allowing the prosecutor to choose which atrocity committers to indict and which to ignore is a possible extension of the current model.

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International Criminal Regime 949

to any leader under indictment. This latter assumption is not a necessary feature of the model because, as I shall show, the foreign state's behavior is the same regardless of whether it is a member of the regime or not; however, the assump- tion does allow a discussion of the foreign state's compliance with the regime. The introduction of the prosecutor changes the game form, which is illustrated in Figure 4, in one respect-the leader can now surrender to the prosecutor. If the leader surrenders to the prosecutor he or she will suffer a punishment with an expected present value of -m E (-r,0).26

The expected present value of asylum is normalized to 0; however, leaders may still be willing to surrender to the prosecutor if the foreign state turns down their request for asylum because by doing so they avoid retribution from their domestic

political rivals. Indeed there is a cutoff value of at, which I call d, for which leaders are indifferent between surrendering to the prosecutor and attempting to remain in power. I also define another cutoff value of a,, q, which is the value of at for which leaders are indifferent between stepping down and not doing so if they receive asylum from the foreign state. Obviously & < t; that is, the proba- bility of survival for which leaders would be willing to step down and be pun- ished must be lower than the probability for which they are willing to step down with impunity.

An important feature of the game is that it does not give the prosecutor any means of enforcing its indictment on the foreign state. The foreign state does not pay any costs for granting the leader asylum. Obviously this is an extreme assump- tion; however, it does have some basis in fact. The Rome Statute contains several loopholes that allow members fairly wide latitude as to whether they must comply with the Court's requests, and the ICC has no explicit enforcement provisions. The Court must rely on the cooperation of its members.27 Most importantly, many states have yet to sign the Rome Statute so they are in no way obligated to comply with its indictments.

Without any higher authority to enforce the foreign state's compliance with the new institution, all commitments that the foreign state has made by joining it must be self-enforcing-the foreign state cannot obtain higher utility from accepting the leaders' requests for asylum than it does from rejecting them. Still, the addi- tion of the prosecutor alters the foreign state's incentives in important ways. First, while the foreign state still has a strictly dominant strategy to accept leaders' requests for asylum when at > 6, the foreign state no longer does when at < i,

26. Admittedly there may be some uncertainty as to whether the leader will actually be convicted after he turns himself in, and there may also be some ambiguity a priori about what the leader's pun- ishment will actually be in the end. I abstract from those complications here. I also do not consider the possibility that the prosecutor may negotiate a "plea bargain" with the leader in which the leader sur- renders and receives a payoff with an expected present value less than zero but still greater than -m. As discussed below, there are circumstances in which allowing such a possibility will enhance the deterrent effect of the institution.

27. Henquet 1999.

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950 International Organization

1. N

Choose leader

2. N

draw at

3. Li Atrocities No atrocities

4. Li 8Request

asylum Do not request asylum

Li deposed 6. Return to Reject Accept

Li survives node 1 5.N 7. N Retum to

node 1

Li survives Li deposed Return to Return to node 2 node 1 Li survives Li deposed

Return to Return to Postindictment 9. N node 2 node 1 subgame

draw al

10. Li

12. Li Return to Donot node 1.

13. N

-m, U

Return to Li survives Li deposed node D Return to Return to

node 9 node 1

L survives L t deposed Return to Return to node 2 node 1

FIGURE 4. Game form of the stage game, with institution

because when leaders' probabilities of survival are that low, leaders will actually surrender to the prosecutor if the foreign state rejects their request. Therefore, when leaders' probabilities of survival are that low, the foreign state is rid of them whether it accepts their requests or not. Note that if the foreign state complies with the

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International Criminal Regime 951

prosecutor's indictment it is not doing so to avoid punishment from the regime's other members, because by assumption there are no such punishments. Instead, the foreign state complies simply because it is costless to do so. In fact, because it is costless to comply with the prosecutor's indictment, when leaders' probabilities of survival are that low, the foreign state may as well do so regardless of whether it is a member of the regime or not.

The effect of this change on the foreign state's behavior may in turn affect lead- ers' behavior. I say "may" because the effect depends on leaders' beliefs about what the foreign state will do if a value of a, < & is actually drawn. If leaders do not believe that the foreign state will reject their request in those circumstances, the regime will have no effect on their behavior. However, if leaders believe that the foreign state will comply with the regime when it is costless to do so, their expected present value of committing atrocities will be reduced. Before the cre-

ation of the regime, leaders' expected present value if Nature drew at < & was 0, because the leader would obtain asylum in the foreign state under such circum- stances. Under such beliefs, leaders' expected present value if Nature draws a, in that range is lower as a result of the regime (namely -m < 0). The possibility that leaders may be forced to accept punishment for atrocities if Nature draws a suffi- ciently low value of at reduces their expected present value of committing atroc- ities, and therefore makes it less likely that they will do so in the first place. Specifically, the value of at that Nature must draw to make it worthwhile for the leader to commit atrocities is higher and therefore less likely to be drawn.

Figure 5 illustrates what might be called the "total" effect of the new regime on leaders' expected present value of committing atrocities when leaders believe the foreign state will reject their request for asylum when it is costless to do so. There

is a direct effect and an indirect effect. The direct effect is that for values of at < & leaders will surrender to the prosecutor and receive a punishment with an expected present value of -m rather than 0. The indirect effect is the reduction in leaders' expected present value of being in the postindictment subgame, as compared to the postatrocities subgame before the creation of the regime. This indirect effect in turn causes an increase in the value of at for which leaders will request asylum from a to a and a downward shift in leaders' expected present values for draws of at > a. The total change in the expected present value as a result of the direct and indirect effects can be found by integrating the expected present value in each of the two scenarios (pre- and postregime) over all possible values of at. As shown in Figure 5, the total expected present value of committing atrocities is smaller by the amount of the gray shaded area as a result of the institution and therefore leaders are less likely to commit atrocities in the first place.

Discussion

A few points are worth highlighting to clarify the model and its results. First, the model points to a problem with the criticism, mentioned in the introduction, that

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952 International Organization

1+6U-------------------------------------- 1 +bU

Li's EPV prior to the creation of the

regime

Li's EPV following the creation of the

regime

0 .--------------------------

ON:

S will not S will Li will not request exile for a, in this range. accept accept L-'s Li's request obr request asylum for for asylum values of for values at in this of a, in this range. range.

FIGURE 5. Total effect on the regime when Li believes S will comply when at < &

the ICC will fail to deter because it has no enforcement power. That criticism assumes that foreign military or economic intervention is the only way human rights abusers may be brought to justice, but of course that is not the case. As Akhavam put it:

[P]olitical ... fortunes change, and the seemingly invincible leaders of today become the fugitives of tomorrow. Whether their downfall comes through polit- ical overthrow or military defeat the vigilance of international criminal jus-

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International Criminal Regime 953

tice will ensure that their crimes do not fall into oblivion undermining the prospect of an easy escape.28

The mechanism modeled in this article is akin to the one that Akhavam describes.

The institution modeled here has no means of sanctioning either atrocity-committing leaders or the states that offer them sanctuary. Despite the extreme weakness of enforcement powers for both the institution and foreign states, the institution may, in the right circumstances, still have some deterrent effect because leaders may recognize that a time may come when their best option is surrendering to the inter- national prosecutor. Under those circumstances they may have little hope of obtain- ing asylum because states have no incentive to offer it. Indeed, the record of the International Criminal Tribunal for the Former Yugoslavia provides some exam- ples of this process at work. As of 2003, of the sixty-nine indicted war criminals in the custody of the ICTY or on provisional release, a plurality (twenty-seven) surrendered voluntarily.29

A second implication of the model is that the number of periods in which atroc- ities are committed will not increase as a result of the creation of this institution.

This result is in stark contrast to the concerns mentioned in the introduction that

fear of prosecution will induce some atrocity-committing leaders to hold on to office longer than they otherwise would have. The institution potentially reduces leaders' expected present values of committing atrocities, which in turn means that leaders are less likely to do so in the first place (Nature will have to draw a higher at for them to choose to do so). In doing so, however, the institution does not prolong the reign of leaders who have committed atrocities. As I show in the

Appendix, the cutoff point of at (leader's probability of survival), below which the leader will step down, cannot be lower with the institution than without it and in general it will be larger. In other words, the institution modeled here will not increase the number of periods of atrocities and may reduce them.

The motivation for this criticism is the realization that leaders will be less will-

ing to step down if they are going to be punished for their crimes than if they will not be punished. Those incentives are illustrated by a comparison of &~, the maxi- mum value of a, for which the leader would be willing to surrender to the pros- ecutor, and a, the maximum value of a, for which the leader would be willing to step down if granted immunity. The former is unambiguously lower than the lat- ter; meaning that the range of a, for which leaders would be willing to step down and be punished is smaller and therefore less likely to be drawn from. The point is that surrendering to the prosecutor is not the only way that leaders who have com- mitted atrocities might leave office even after the creation of the new regime. For- eign states may still agree to grant asylum if it is the only way to get rid of an atrocious dictator.

28. Akhavam 2001, 7. 29. International Criminal Tribunal for the Former Yugoslavia 2003. Of the remainder, twenty-four

were detained by international forces, eleven were arrested by Serbia, and seven were turned over by other states. Eighteen remain at large.

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This criticism appears to be based on one of two assumptions. The first is that states will comply with the Court's indictments even when it is not in their inter- ests to do so. Under this assertion, mutually beneficial asylum agreements between beleaguered dictators and foreign states will be foregone because they would be contrary to the requirements of the ICC. In this model, states only comply with the institution's indictments when it is costless to do so; that is, when doing so offers them at least as high an expected present value as not doing so. On occa- sion (when a, < 2), states may refuse to offer asylum but only because they know that the leader will surrender to the prosecutor anyway. The scenario in which the reign of atrocity-committing leaders is prolonged cannot occur in this model because in such a case, states would simply not comply with the indictment and would offer the dictator asylum.

Alternatively, this criticism could be based on the assumption that the ICC has some enforcement power-that it can impose costs on states that do not comply with its indictments or somehow make it easier for other states to do so. If the ICC had

such power then the kind of asylum agreements between a leader and a foreign state modeled here would become impossible because they would no longer be credi- ble.30 The leader would know that the foreign state would not comply with its asy- lum agreement and therefore would not request one in the first place. Some leaders' reigns would indeed be prolonged because such leaders would cling to power even when their probabilities of surviving in office fell below the cutoff point, a.

The assumption that the ICC has such enforcement power is problematic. Indeed, the ICC's lack of enforcement power is one of the central criticisms of the regime as discussed above. More importantly, membership in the ICC, while fairly broad, is far from universal. States that are not members of the ICC have not committed

themselves to comply with the prosecutor's indictments and have no legal respon- sibility do so. Of course, individual states and the UN Security Council can always impose sanctions or other punishments on a country for harboring atrocity com- mitters, but those entities had that option before the creation of the ICC and the creation of the ICC does make it any easier or less costly to avail themselves of that option. The point is not that commitment problems do not exist, but that there is nothing to indicate that the ICC will make them more severe.31

30. The timing of the costs is important. If the foreign state were to pay one-time costs for making such an agreement, then agreements would still be possible if those costs were not too high. Such costs would be paid once, at the time the leader went into asylum, and therefore would be irrelevant to any future decision making. The scenario discussed above is a case where the ICC is somehow able to impose costs after that dictator has gone into asylum. The foreign state cannot credibly accept a request for asylum in those circumstances because it has a dominant strategy to turn the leader over to avoid such costs.

31. Suppose, however, that the creation of the ICC does, despite all of the indications to the con- trary, make punishing states that harbor atrocity committers easier-including states that did not even sign the Rome Statute. The effect of the ICC is ambiguous in such a case. The deterrent effect of the ICC would make atrocities less likely. That effect would be offset by the effect of prolonging the reign of atrocity committers. Which of these effects will dominate is unclear.

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International Criminal Regime 955

Third, the model has implications for the criticism that ICC will create a sys- tem of "Cadillac justice" in which leaders are tried fairly by the ICC and low- level perpetrators are subjected to harsh and unfair trials at home. The point of this criticism, which was raised by Roth, among others, is mainly normative- such a result is unfair on its face.32 However, such a system would also be det- rimental to deterring atrocities. If the ICC were able to compel domestic political agents to turn over deposed atrocities perpetrators to the ICC, the deterrent effects described in the model would disappear. The issue is the severity of punish- ments. The ICC is barred from handing down a death sentence-something many atrocity-committing leaders would face from domestic political rivals. If leaders knew that their domestic opposition would be forced to turn them over to the ICC if they were deposed, the effect on deterring atrocities and on leaders' incen- tives to step down would be the same as reducing the value of r, the comparative statistics of which I explored in Figure 3, and the ICC could actually lead to more atrocities according to this analysis.

Fourth, the institution in this model does not really do anything. The prosecutor merely waits for human-rights-abusing dictators to surrender to the Court. As such, this analysis may beg the question: why did the world need an ICC at all? It is true that what the institution modeled here accomplishes could be accomplished sim- ply by states pledging not to harbor human rights abusers unless those abusers pay some agreed-on punishment (recognizing that states will fail to comply with those

pledges when at - E&). However, such a treaty would still leave the practical prob- lem of whom the leader would surrender to and who would extract the "payment" of -m. These tasks could have been delegated to a state member of the agreement, but the creation of a prosecutor's office seems as good a choice as any.

Fifth, the model has implications for a potential problem that participation in the regime is far from universal. Will nonmembers of the ICC make the regime irrelevant by continuing to offer atrocity-committing dictators asylum? This model suggests that there is no reason for them to do so as long as those leaders' proba- bility of surviving in office is sufficiently low. The effect of the regime in this model is not the creation of some enforcement mechanism that induces the regime's members to comply with their treaty obligations. Rather, the effect of the regime is the creation of an international agent to whom atrocity-committing dictators can surrender and who can hand out punishments to those dictators. The regime fulfills a jurisdictional gap that previously existed in international criminal law. A country that is not a member of the regime has no less incentive to refrain from offering a leader asylum than does a member of the regime.

A sixth point is that it may appear that the problem of atrocities is too easily solved in this model. If the international community wants to eliminate atrocities,

32. Roth 2002. This criticism was raised about the Rwandan tribunal in particular. Because of this and other problems with the tribunal, the Rwandan government actually voted against the establish- ment of the tribunal; see Akhavam 1996; and Henquet 1999.

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all it has to do is set the punishment handed out by the prosecutor (m) at a high level, which will produce a large reduction in the expected present value of being in the postatrocities subgame, and atrocities will be deterred. However, that inter- pretation of the role of m in the model would be incorrect; m is the cost of pun- ishment to the outgoing leader. The prosecutor does not really have that much control over that parameter. The prosecutor has limitations on how harsh a pun- ishment it can set, and the prosecutor cannot alter the leader's valuations of cer- tain outcomes. Regarding the ICC in specific, life in prison is the worst punishment that it can hand down, and it is likely that that punishment is simply not that bad compared to what many leaders could expect to receive from their domestic oppo- sition. I might also mention that the model implies that making m very large would lead to more offers of asylum.33

Finally, the model suggests a possible role for plea bargaining. Before the cre- ation of the institution in this model, leaders who draw a, less than a enter into an asylum agreement and receive a payoff with a present value of 0. Such leaders are receiving a surplus from asylum. They would have actually been willing to "pay"

in some sense for asylum but are not required to do so. The lower their value of at is, the greater their surplus from an asylum agreement. Following the creation of

the institution, leaders with sufficiently low values of at are required to "pay" through the imposition of punishment cost m. It is the prospect of this "payment" that reduces the expected present value of committing atrocities and thereby deters some marginal human rights abusers.

Granting the prosecutor some ability to make "plea bargains" could actually enhance the deterrent effect of the institution in this model. If the prosecutor were allowed to make such agreements, he or she could tailor the punishment to each

leader's value of at, thereby obtaining some punishment from every leader who draws a sufficiently low at that their expected present value of holding office is less than 0. Via these plea-bargained punishments, leaders would be required to "pay" so that they obtained no surplus from the plea agreement. The prosecutor would be playing a role akin to that of a price-discriminating monopolist. All lead- ers who drew an a, that offered an expected present value of staying in power less than 0 would be punished to the maximum extent possible while still being induced to step down, so that the expected present value of committing atrocities in the first place would be even lower, and the deterrent effect would be greater.34

Conclusion

The model in this article considers the effects of an ICC-like institution on the

strategic interaction between an atrocity-committing leader and a foreign state that would like to facilitate the transition to a more palatable leader. Before the cre-

33. I thank Lisa Martin for pointing this implication of the model out to me. 34. Unfortunately the plea bargains would have to be tailored to the leaders' probability of political

survival and not to the severity of their crimes.

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International Criminal Regime 957

ation of the institution, foreign states strictly prefer accepting any request for asy- lum from an atrocity-committing leader, and following the creation of the regime they no longer do in certain circumstances. If the leader is so likely to lose power that he or she would willingly accept punishment by the regime in return for pro- tection from domestic political rivals, the foreign state has no reason to offer the leader asylum because regardless of whether it does or not, the atrocity-committing leader will step down.

The analysis addresses certain criticisms of the ICC in the literature. First, it provides some conditions under which the ICC may deter atrocities at the margin despite its lack of enforcement power. Second, the institution does not prolong the reign of atrocious leaders, as some commentators have worried. Leaders who would step down if granted asylum but who would not step down if forced to be pun- ished for their crimes are granted asylum in this model. The only leaders who are actually punished in this model are those who willingly accept punishment to avoid retribution from domestic political rivals. As such, their reigns are not prolonged.

In addition to these policy considerations, the article makes a theoretical con- tribution to understanding the necessity of enforcement for the effectiveness of international regimes. The model provides an example of a regime that is effica- cious despite the fact that none of the usual trigger strategies are employed to insure compliance. The institution deters atrocities under specified conditions even though foreign states never intervene to depose atrocity-committing dictators. Most interestingly, foreign states occasionally comply with the indictments of the pros- ecutor even though there is no punishment for noncompliance. Furthermore, the model does not rely on norms arguments or learning, or pressure from domestic constituencies, nor does it assume away the enforcement problem by asserting that it is a management problem.

A natural extension of the argument would be to better model the domestic polit- ical milieu-in particular, the process by which atrocities increase leaders' ability to hold on to power. Recent work by Bueno de Mesquita and colleagues has addressed this topic, although obviously without reference to the ICC.35 Incorpo- rating the features of their model into the one in this article may provide more refined predictions about the likely effects of the ICC, especially with regard to the effect of domestic political institutions.

The main remaining question, of course, is how substantively important the potential deterrent effect discussed in this article will be. As Cameron has pointed out, there is little evidence that making punishments harsher lowers crime rates even within relatively well-functioning domestic criminal justice systems.36 What hope is there, then, of a substantively important impact from the ICC? Ultimately that question is an empirical one and can only be answered prospectively by param- eterizing the model from real-world cases, which is the subject of ongoing empir- ical work. In the meantime, I hope that this article will inform the continuing legal

35. Bueno de Mesquita et al. 2003, chap. 8. 36. Cameron 2004, 92-93.

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958 International Organization

debate such that the ICC is no longer characterized as either a cure-all or a catastrophe-in-waiting. If this model is any guide, the ICC will be neither of those things. It will not be an institution that does absolute harm and it may do some good. The extent of that good remains to be determined.

Appendix

Basic Set-up of the Model

Players are described in main text. I assume the leader (Li) and the foreign state (S) have identical one-period discount rates of 8. Li derives per period utility of 1 from holding office and per period utility of 0 from not being in office. In the absence of atrocities by Li, S's per period payoff is 1, unless Li has committed atrocities, in which case S's per period utility is u < 1. S does not care whether Li holds onto power or is deposed, only whether atrocities have been committed or not.

If Li commits atrocities and is subsequently removed from office, Li suffers a one-time retribution cost of -r < 0, leaves office and the game ends for Li. If Li is deposed not having committed atrocities, he receives a one-time payoff of d E (-r, 1) and the game ends for him. If Li goes into exile the game ends for him, but he avoids the retribution cost, - r, and does not receive the one-time payoff from being deposed, d. Once Li leaves office, either by being deposed or stepping down, the game ends for him, he has no prospect of returning to power and he receives a payoff of 0 each period from that point forward.

Nature (N) chooses the probability that Li will keep power in a given period if Li com- mits atrocities. I call this probability at where t indexes the current period. This probability is chosen from a known distribution F(a), with support [0,1] and associated density f(a). The value of at is common knowledge among all players. The probability that the leader holds on to power if he does not commit atrocities is fixed at q.

The game form of the stage game, which corresponds to the complete reign of a given leader, Li, and as such may cover several periods, is illustrated in Figure 1. The game form for the reign of a given leader after the first period in which he commits atrocities, which I refer to as "the postatrocities subgame," is shaded gray. The remainder of the game form in Figure 1 corresponds to "the preatrocities subgame," which is the subgame up to and includ- ing the first period (if any) that Li commits atrocities.

Play proceeds over discrete time periods t E {1, 2, 3...}. In the preatrocities subgame the following moves occur sequentially in each time period. N chooses the probability that Li will be deposed if he commits atrocities. Li then decides whether or not to commit atroc- ities. If Li decides not to commit atrocities he can request asylum. The foreign state then decides whether or not to accept the request. If the foreign state accepts the request, Li steps down and the game ends for L;, returning play to the beginning of the preatrocities subgame. If the foreign state rejects the request, Li faces a lottery in which he keeps power with probability q and is deposed with probability 1 - q. If instead Li decides to commit atrocities, he faces a lottery over his political survival.37 If Li does not survive, play returns

37. A straightforward alteration of the game would be to allow Li to request exile after committing atrocities in the preatrocities subgame. Doing so would be superfluous, however, because if Li is plan- ning to step down and go into exile in the first period of his reign, there is no reason to commit atroc- ities before doing so.

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International Criminal Regime 959

to the beginning of the preatrocities subgame. If Li survives, that lottery play proceeds to the postatrocities subgame.

Sequence of play is similar in the postatrocities subgame. N chooses the probability that Li will be deposed. Li then decides whether to request asylum or not. If Li does not request

asylum he faces a lottery over his political survival-he survives with probability at and is deposed with probability 1-a,. If Li does request asylum, the foreign state then decides whether to accept the request or not. If the foreign state accepts, Li steps down, the game ends for him, and play returns to the beginning of the preatrocities subgame. If the foreign state chooses "reject," Li faces a lottery over his political survival as described above.

I employ Markov perfect equilibrium (MPE) as a solution concept.38 MPE is appropri- ate because there is a stochastic component to the game-the realization of future draws on the dictator's probability of political survival-but no asymmetric information about the realizations of that variable once drawn. I use MPE purposefully to illustrate the efficacy of the regime without the use of trigger strategies. Trigger strategies are not possible in a MPE because players use only payoff-relevant information, not information about previous moves. I present the results via a series of lemmas. Proofs of these statements follow from straightforward application of sequential rationality and are therefore omitted.

Solving the Postatrocities Subgame

The only slight wrinkle in solving the postatrocities subgame is S's incentives at the last node of the game, which can be summarized as follows:

Lemma 1: If at > 0 and if there exists at+l E (0,1] such that Li+1 will refrain from committing atrocities, S has a strictly dominant strategy to accept Li's request for asylum.

The intuition for the result is that if S accepts Li's request for asylum, then, with some

probability p > 0, which I describe in greater detail below, S will obtain a payoff of 1 in the subsequent period and obtain a payoff of u < 1 with probability 1 - p. If, however, S

rejects Li's request, S will obtain a payoff of 1 only with probability p(1 - at). The impor- tant point is that S has a strictly dominant strategy to accept Li's request for asylum prior to the creation of the regime. MPE is crucial to this result, because it assumes players respond only to payoff-relevant information. As such, by rejecting a request for asylum, S does not change future leaders' beliefs about what it will do in the future, and therefore does not deter future atrocities.

Turning to Li's decision at the second node of the postatrocities subgame, Li's expected present value (EPV) of not requesting asylum at that node is:

U, = a,(1 + r + 8U) - r (1)

Unsubscripted U in equation (1) is a constant, the formula for which is:

fa + 5(1 + r) - [1 - F(a)]r U = f(a)a(1 + r + rU) - rFda = 1 - ?

38. Fudenberg and Tirole 1991, chap. 13.

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960 International Organization

where ^ = f f(a)a da, and a is defined below. U is Li's EPV from the next period (before at+ is known) forward of being in the postatrocities subgame-that is, U is Li's EPV at the first node of the postatrocities subgame.

If the EPV in equation (1) is less than or equal to 0, Li will request asylum, the EPV of which is normalized to 0, S will accept, and Li will step down. Leaders will not step down voluntarily until a sufficiently low a, is drawn. If a leader is going to be willing to request asylum the following must be true:

r

a, < = a (2) l+r+8U -

Lemma 2: In any MPE of the game, the outcomes of the postatrocities subgame are:

1. If a, ?- a q, Li does not request asylum and survives with probability at. 2. If a, < a, Li requests asylum, S accepts, and Li steps down.

Solving the Preatrocities Subgame

I begin the discussion of this subgame with S's decision to accept or reject a request for asylum. For ease of exposition, define S's EPV from node 1 forward as f1 and define S's EPV from node 9 forward as W. ft is S's EPV when there is a new leader and W is S's EPV

when it is already in the postatrocities subgame. More formally:

W = ff(a)(u + M1) da + fa(a)(a[u + 8W) + (1 - a)(u + 3f1)]da

u + 8(1 - a)f

1 -(3) and

p + (1 - p)(u + 6W) l = p(l + 8f1) + (1 -p)(u + 1W) = (4) 1 - pa

where p is the (constant) probability that N will draw a sufficiently low a, in the next period that Li will refrain from committing atrocities in that period. Equations (3) and (4) can be

combined to solve for values of W and f1 solely as functions of the constants p, u, a and 8, and therefore W and f1 are themselves constants.

If Li has yet to commit atrocities, S has a weakly dominant strategy to accept a request

for asylum. S's payoff from accepting such a request is 1 + 310. The highest payoff that S can receive from rejecting a request for asylum in the preatrocities subgame is 1 + q(8fl) +

(1 - q)86f = 1 + 31Q. This is the substantively uninteresting case where Li does not commit atrocities and steps down in the first period of his reign, so I simply stipulate that all such requests are accepted.

Turning to Li's decision at the third node of the preatrocities subgame, Li will commit atrocities if the EPV of doing so is higher than the EPV of not doing so. Li's EPV of not committing atrocities in the current period is:

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International Criminal Regime 961

SMax [1 + (1 -p)U] + (1 - q)d (5) 1 - p~q

Li can guarantee an EPV of 0 by stepping down in the first period. If the first term in the curly brackets is negative (which could happen if d or U were negative and large enough in magnitude) then the highest payoff that Li can receive when he does not commit atrocities is 0, which he obtains by stepping down. In such a case, Li will either not commit atrocities

and step down, or if at is high enough, Li will commit atrocities. A necessary condition for Li to choose to commit atrocities is that the EPV in equation

(1) is higher than the EPV in equation (5). This will be the case if:

r 1

a, > + + - Q r - U (6) 1+r+8U l+r+8U

As indicated, this is only a necessary condition--obviously it must also be true that at > q since L; would not choose to commit atrocities if it lowered his probability of keeping office. Li will commit atrocities if at > 5. Notice that 5 = - if the first term in the curly brackets in equation (5) is negative. In such a case Li would commit atrocities only if at > a = C, which by definition is the value of at for which the EPV of committing atrocities is equal to 0. Li will never commit atrocities in the preatrocities subgame if the EPV of doing so is negative because he can guarantee a higher EPV (0) by not committing atrocities and stepping down. Incidentally, p is the probability that at -< .

Lemma 3: In any MPE of the game, the outcomes of the preatrocities subgame are:

3. If a, > 6-, Li commits atrocities and proceeds to the postatrocities subgame.

4. If at <: 5, Li does not commit atrocities and:

q[1 +8(1 -p)U]+ (1 -q)d 4a. If < 0, Li requests asylum, S accepts and Li steps

1 - pbq down, or

q[1 + 6(1 -p)U] + (1 - q) d 4b. If > 0, Li does not request asylum and survives

1with probabil - pity q.

with probability q.

Outcome 4a is the substantively uninteresting case where Li steps down and goes into exile in the first period of his reign. This occurs when Li's EPV of remaining in office is negative whether he commits atrocities or not. I will ignore this outcome for the remainder of the Appendix.

Adding an International Criminal Regime

Now suppose an international institution that is staffed by a nonstrategic actor P (the pros- ecutor) is created. P automatically indicts any leader who commits atrocities. The game form of the preatrocities subgame is unaltered by this change, but the postatrocities sub-

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962 International Organization

game is amended as indicated by the game form in Figure 5. I will call this subgame, the game form for which is shaded in gray in Figure 5, the "postindictment subgame" to dis- tinguish it from the postatrocities subgame discussed above.

The postindictment subgame begins just as the postatrocities subgame did, with a draw of a, by N. Li then chooses whether or not to request asylum. If Li chooses not to request asylum he is then faced with a lottery over his political survival in the usual way. If, how- ever, Li requests asylum, he presents S with a choice to accept or reject that request. If S accepts Li's request, Li steps down and the game ends for Li as described previously. If S does not accept Li's request, then Li must choose whether to surrender to P and receive, with certainty, a one-time penalty of -m E (-r, 0). If Li surrenders he steps down, return- ing play to the beginning of the preatrocities subgame. Alternatively, Li can choose not to surrender, in which case he takes his chances at holding onto office according to the usual lottery.

Solving the Postindictment Subgame

I will begin the discussion of equilibria in this new situation with Li's decision at the last node of this subgame where S has turned down his request for asylum. Li's EPV of not surrendering at that point is:

Ui, = a,(l + r + 80)- r (7)

Unsubscripted U in equation (7) is Li's EPV in the next period (before a,t+1 is known) of

being in the postatrocities subgame in this new situation following the creation of the regime. It is Li's EPV at the first node of the postindictment subgame. U is a constant, the value of which depends on Li's beliefs about what S will do in the future, as discussed below.

Define:

r

a = (8)

as the level of a, for which Li would be indifferent between stepping down and not step- ping down, if he could obtain asylum from S in this new situation following the creation of the regime. It is the value of a, for which Li's EPV is 0 in this new situation. The only difference between a and a is that a has U in the denominator rather than U. I also define

a new cutoff point:

r-+8

1 +r+8U

This is the value of a, below which Li would be indifferent between surrendering to P and attempting to stay in power. Li's EPV from surrendering to P is -m, so ~ corresponds to the level of a, for which Li's EPV of attempting to stay in power was -m. If a, < 5, Li would prefer surrendering to P rather than attempting to stay in office, if S rejects his request

for asylum. If a, E [&,g], Li would not be willing to surrender to P but would be willing to step down if he received asylum. If a, > a, Li would be unwilling to step down even if granted asylum by S.

Turning to S's decision of whether to accept Li's request, the foregoing discussion implies

that while S still has a strictly dominant strategy to accept Li's request when at 2 --, it no

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International Criminal Regime 963

longer has a strictly dominant strategy to accept Li's request for asylum when a, < j, because Li would be willing to surrender to P. S is indifferent between rejecting and accept- ing Li's request under those circumstances because, regardless of whether it accepts or not, Li will step down. Therefore Li can no longer be certain that S will accept his request for asylum. This is true regardless of whether S is actually a member of the agreement or not- that is, regardless of whether S has formally committed itself to comply with P's indict- ments or not. To summarize, the same two outcomes that occurred in the postatrocities subgame without the regime also occur, mutatis mutandis, in the postindictment subgame; however, in addition there is a new outcome in the postindictment subgame in which Li surrenders to P. These outcomes are formalized in the following lemma.

Lemma 4: In any MPE of the game, the possible outcomes of the postindictment sub- game are:

1'. If at - !, Li does not request asylum, and survives with probability at,.

2'. If i ?- at < a, Li requests asylum, S accepts, and Li steps down. 3'. If a, < &, Li requests asylum, and either:

3a'. S accepts, and Li steps down, or

3b'. S refuses, and Li surrenders to P.

The significance of 3b' is that, despite P's lack of enforcement power, some atrocity

committers may surrender to him. For low enough values of at, S will be indifferent between accepting Li's request for asylum and rejecting it, because S knows that even if it rejects the request, Li will surrender to P and step down. This is in contrast to the outcome in the previous section where S clearly had a dominant strategy to accept Li's request.

Note that there is some ambiguity about the equilibrium when a, < d. S is indifferent between accepting and rejecting Li's request for asylum in those circumstances because either way Li will step down. In a MPE, S has no reason to reject Li's request for asylum for the purpose of sending a signal to leaders Li+1 and beyond because in MPE, players only make decisions based on payoff-relevant information. If I had assumed that S gets some very small utility increment, E, from seeing atrocity committers punished, it would eliminate this ambiguity and make rejecting such a request a dominant strategy for values of a, in the neighborhood of & and below. However, I do not make that assumption because it seemed ad hoc.

Solving the Preatrocities Subgame

The structure of the preatrocities subgame is identical to that of the subgame prior to the creation of the regime. As in the previous case, I will set aside the substantively uninterest- ing question of S's decision to offer asylum in this subgame, if asked.39 I turn instead to Li's incentives to commit atrocities. Differences in Li's decision (if any) arise only because of changes in his EPV of committing atrocities now that there is the possibility that he

39. This is the case in which Li requests asylum in the first period of his reign. As before, the foreign state has a weakly dominant strategy to accept such a request, and so to dispense with this case I stipulate that it always does.

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964 International Organization

could be punished for doing so if N draws a sufficiently low at. That EPV will depend in turn on Li's beliefs about what S will do if at < ii. I will dispense with the obvious case first: if Li believes that S will grant him asylum when at < & (in other words, he believes that equilibrium 3b' will not occur), then the effect of the new regime on the equilibria in the preatrocities subgame will be nil. Li's behavior will be identical to that described in the previous section.

If however Li believes that outcome 3b' will occur if N draws a low enough at, then his behavior in the preatrocities subgame will be quite different because his EPV of commit- ting atrocities will be lower and this in turn will affect the cutoff values of at for which he would be willing to commit atrocities. At the third node of the preatrocities subgame, Li's EPV of choosing to commit atrocities is given by equation (7) where, given these beliefs:

U = -mf f(a)da +f f(a)[a(l + r+ U) - r]da

a(1 + r) - [1 - F(d)]r - F(g)m ,and

S= f(a)a da analogous to a in the previous section.

Li's EPV of not committing atrocities at that node is:

Max{q[1+6(1-p)]+(1 - q)d(9) 1 - pfq

where / is the (constant) probability that N will draw a sufficiently low at in the next period that Li will choose to refrain from committing atrocities. The new regime has no effect on

Li's payoffs if he never commits atrocities because d and q remain fixed. The only differ- ence in Li's EPV of not committing atrocities compared to the earlier case is in the change

from U to U and from p to p. As before, Li will commit atrocities if the EPV of doing so exceeds the EPV of not

doing so-that is, if equation (7) is greater than equation (9). I define & as the value of at that makes these two equations equal, analogous to 5 in the previous section. According to the same line of argument in the previous section, Li will commit atrocities if N draws and a, > 5. I summarize these possible outcomes in Lemma 5.

Lemma 5: If Li believes that equilibrium 3b' will occur when at < i, the possible out- comes of the preatrocities subgame following the creation of the regime are:

4'. If at > 5, Li commits atrocities and proceeds to the postindictment subgame.

5'. If at - 5: , Li does not commit atrocities and:

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International Criminal Regime 965

q[1 + 8(1 -P) 0] + (1 - q) d 5a'. If < O, Li requests asylum, S accepts and Li steps

1 - pSq down, or

q[1 + 8(1 - p)&] + (1 - q)d 5b'. If O, Li does not request asylum and survives

1 - p8q with probability q.

Finally, the analysis shows that the reign of a leader who has committed atrocities will

not be prolonged as a result of the regime modeled in this article. Prior to the creation of the institution, Li would leave power whenever a, < a, and after the creation of the insti-

tution, Li will leave office whenever at < a. Since U - U, a comparison of equations (2)

and (8) shows that a -> a.

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