Political Groups, Leader Change, and the Pattern of International Cooperation

Political Groups, Leader Change, and the Pattern of International CooperationAuthor(s): Alastair SmithSource: The Journal of Conflict Resolution, Vol. 53, No. 6 (DECEMBER 2009), pp. 853-877Published by: Sage Publications, Inc.Stable URL: http://www.jstor.org/stable/20684620 .

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Political Groups, Leader

Change, and the Pattern of International Cooperation Alastair Smith Wilf Family Department of Politics New York University, New York

Nations are politically heterogeneous and which group is in political ascendency

shapes the nature of interstate cooperation through two mechanisms. First, groups dif

fer in the benefits they receive from cooperation. This affects which groups can com

mit to cooperate. Second, a nation may selectively withhold cooperation from one

group to influence the domestic political competition between groups in another

nation. By integrating political competition between leaders of different groups under

different institutional rules into a prisoner's dilemma model of international coopera

tion, the theory generates hypotheses relating leader turnover, group membership, and

patterns of cooperation.

Keywords: cooperation; infinitely repeated prisoner's dilemma; leadership; domestic

political institutions; political groups

There

is great variation in international cooperation. In many instances coopera tion is supported by the threat of mutual retaliation, as prescribed by the liberal

paradigm (Keohane 1984; Axelrod and Keohane 1986). Yet, this adherence to the "rules of the game" is not ubiquitous. On one hand, the United States foregoes

many opportunities to cooperate. This can be a response to past cheating, but in some cases, the United States simply refuses to cooperatively interact with foreign governments and thus cooperative opportunities are foregone. This was a common

pattern during the cold war when the United States distanced itself from communist states. On the other hand, the United States allows some nations to cheat without

consequences. Some governments repeatedly fail to live up to their commitments and obligations and yet go unpunished. Root (2008) documents many such cases. The continuation of foreign aid to friendly nations who repeatedly failed to imple ment promised reforms was especially common during the Cold War. In a similar

vein, there is a growing literature on the enforcement of conditions attached to aid

Author's Note: Earlier versions of this article were presented at the 2007 Peace Science Society, the

2008 International Political Economy Society Meeting, and the 2009 International Studies Association. I

thank the audiences for their useful comments. I also received terrific advice from Kanchan Chandra, James Morrow, and Ken Scheve.

Journal of Conflict Resolution Volume 53 Number 6

December 2009 853-877 ?2009 The Author(s)

10.1177/0022002709344419

http://jcr.sagepub.com

853



854 Journal of Conflict Resolution

and IMF and World Bank programs (Andersen, Hansen, and Markussen 2006; Barro and Lee 2005; Dreher and Jensen 2007; Dreher, Sturm, and Vreeland 2006;

Frey 1997; Thacker 1999; Ruttan 1996; Zimmerman 1993). Friends of the United States get loans with fewer conditions. Furthermore, any such conditions are less

likely to be enforced. In contrast, nations opposed to the United States must agree to more stringent terms and abide by them if they wish to receive assistance.

This article identifies two causes for the variation in patterns of cooperation: the

capacity of different groups within a nation to cooperate and the desire by one

nation to influence which group is politically dominant in another nation. It does so

by integrating three levels of analysis: international cooperation between nations, the survival incentives of individual leaders, and political institutions that shape the nature of domestic political competition between competing domestic political groups.

Consistent with the classic prisoner's dilemma approach to international coop eration (Axelrod and Keohane 1986), the model in this article examines interac

tions between two nations, 1 and 2. Both nations are better off if they cooperate. Yet, each nation can make itself even better off if it exploits the cooperation of the other nation while withholding its own cooperative efforts. Because nations' myo

pic incentives are to cheat, some form of reciprocal punishment strategy, such as

threatening to withhold all future cooperation if cheating occurs?the so-called

grim trigger strategy?is needed if cooperation is to be maintained. Such a strategy sustains cooperation provided nations value the long-run rewards from cooperation

more than the short-term gains from cheating. Such ideas of reciprocal punishment strategies account for the lowering of tariffs, preservation of common pool resources, and solving of other collective action problems. Yet, international coop eration is but one of the many concerns of political leaders.

Although it is convenient to think of interactions between states, this is a fiction. Politicians make policy decisions, not nations. Consistent with a growing trend in the international relations literature, I assume individual leaders make policy deci

sions to further their survival interests (Bueno de Mesquita and Siverson 1995; Fearon 1994; Bueno de Mesquita et al. 1999, 2003; Chiozza and Goemans 2004; Wolford 2007). Nations are not homogeneous. To reflect this, I assume Nation 2 is

composed of two groups, A and B. The citizens in Nation 2 choose their leaders

according to their nation's domestic institutional rules. These rules, which are mod

eled using a simple version of the selectorate theory (Bueno de Mesquita et al.

1999, 2003), affect the ease of leader survival. Although the choice of Nation 2's

leader resides with the citizens of Nation 2, Nation 1 can potentially influence whether leaders from Group A or leaders from Group predominate by selectively cooperating with leaders from one group but not leaders from the other. Such dis

crimination alters the level of benefits that leaders from each group can deliver and so shifts the relative ease with which leaders from each group can retain office.



Smith / Pattern of International Cooperation 855

Group membership is assumed to be exogenous. Furthermore, what differenti ates one group from another does not matter. The citizens of a nation can be divided into groups on the basis of ideology, religion, ethnicity, economics, or lin

guistics. The groups in Nation 2 are taken as given. However, recent scholarship, such as Chandra's (2004) study of ethnic parties in India, suggests that the salient

cleavages that divide people into groups vary endogenously with institutions. Posner's

(2005) study of Zambia illustrates these endogenous cleavages. When Zambia was under a multiparty electoral system, parties organized on a linguistic basis.

Yet, tribal groupings were emphasized during the period of one-party rule. In what follows, I explore the consequences of group membership but not the origins of such groupings.

Although cooperation provides benefits for the citizens of a nation, the benefits need not be spread evenly. If one group gains more than the other, then which

group is in power affects Nation 2's commitment to cooperation. Differences in the benefits that each group derives from cooperation can result in on-again, off-again cooperation: one group can cooperate but the other cannot. Yet, political turnover and differences between the groups in terms of the desirability of cooperation are

not the only reasons for oscillations in the level of cooperation between the states. If Nation 1 prefers one of the groups in Nation 2 over the other, then it is incen

tivized to manipulate the political balance within Nation 2 by selectively promoting or withholding cooperation. Suppose Nation 1 prefers Group A to Group B. This was a common occurrence during the cold war when the United States favored

pro-Western groups over those with communist leanings. As Gowa and Mansfield

(1993) show in the case of trade between alliance partners, friends cooperate more

than enemies. If Nation 1 cooperates with Nation 2 only when Group A is in power, then this shifts the political balance in favor of leaders from Group A. Because

Nation 1 discriminates between groups, only leaders from Group A can deliver the benefits of international cooperation to the citizens on Nation 2. Because the citi zens want these benefits, Nation s strategy of selective cooperation makes leaders from Group A relatively more attractive to the citizens of Nation 2 while at the same time reducing the citizens' desire to retain Group leaders. Discrimination shifts the political balance in Nation 2. Group A leaders survive relatively longer while the expected tenure of Group leaders is reduced.

The value-added of the theory presented here is that it integrates existing approaches into a single coherent framework. Rather than providing one explana tion for why the United States allows its allies to renege on their commitments without punishment, another for the proliferation of trade openness between

democracies, and a third for the maintenance of sanctions that fail to obtain policy concessions, the theory provides a single account for these different patterns of behavior. It also identifies the conditions under which each eventuality is likely and characterizes the domestic political consequences in each case.




In addition to this synthesis, the theory also generates a series of novel hypotheses regarding interstate relations and the turnover of political leaders. The ability to build and test theory is greatly increased by examining more questions on different dimen sions. For instance, it has been well established that democracies cooperate more with each other than do other pairs of states (e.g., Leeds 1999; Russett and Oneal

2001). Yet, there are many competing explanations for this phenomenon. To distin

guish between these various explanations, we need to examine dimensions on which their predictions differ. To date there are very few analyses of the relationship between the pattern of interstate interactions and leader change. McGillivray and Smith (2004, 2008) are exceptions. They find that leader change has relatively little effect on relations between democracies. Yet, if an autocratic leader is replaced, then relations tend to sour slightly if relations had previously been good and improve sub

stantially if relations had previously been poor. Although establishing a link between leader turnover and cooperation, McGillivray and Smith treat all leaders as identical and representing the same constituency. Therefore, they cast no light on whether the

empirical effects of leader turnover on the level of cooperation is the result of any shift in leadership or, as indicated by the theory presented here, whether changes in

cooperative relations are more likely when leadership changes results in a different set of societal groups being represented. The theory identifies two mechanisms via which political change causes cooperation to falter. First, the newly installed group does not have the capacity to cooperate; second, other nations discriminate and selec

tively cooperate so as to influence the competition between groups. When a foreign nation dislikes a group that comes to power, it withdraws its cooperation. I illustrate these mechanisms in the following.

Nations are composed of different political groups. Political change leads to dif ferent interests being represented. Shifts in preferences alter policy choices and the interactions between states (Simmons 1994). Consider sovereign debt. Tomz

(2007) suggests nations need to maintain a reputation for paying their debts if

they wish to borrow cheaply. Yet, a national trait for honest dealings is not suffi cient. Each domestic group trades off short- and long-run gains differently, as

Stasavage's (2003) examination of British sovereign borrowing after the Glorious Revolution shows. The Liberal party represented economic groups that benefited from trade and economic openness. As a consequence, the Liberals were com

mitted to loan repayment to keep financial and economic markets open. They could borrow at very low interest rates. In contrast, the cost of borrowing increased under the Tory party. The Tories represented the landed class, which gained relatively less from the expansion of trade. With less vested in future cooperation, Tory lea ders were more likely to repudiate British debt, which meant they had to pay a risk

premium to borrow. Shifts in the pattern of international cooperation can also be driven by the desire

of one nation to influence political competition in another state, as illustrated by the case of U.S.-Iranian relations. In the 1940s and 1950s, various groups




competed for political ascendancy. The United States preferred the pro-Western group to nationalist and Islamic groups. The pro-Western interests were led by Shah Mohammad Reza Pahlavi. The shah had been put on the throne by the British and Russians who had invaded Iran and deposed his father for having pro-Nazi sympathies in 1941?another, although more extreme, example of nations adopting

policies to influence which group is in charge in another nation. The shah faithfully

represented pro-Western interests, but by 1951, he had been sidelined and national ists groups became politically dominant. Prime Minister Mohammad Mossadegh reversed pro-Western policies. His most radical policy was the nationalization of the predominantly British-owned Anglo-Iranian Oil Company?the predecessor of BP. The British refused to cooperate with Mossadegh's government, withdrew all

technical support for the oil industry, and blockaded Iranian ports. As a conse

quence, Iran's oil production collapsed. Average daily production plummeted from more than 550,000 barrels in 1950 to less than 30,000 barrels in 1952 (OPEC 2002). With it disappeared the more than 16 million pounds sterling the AIOC paid to the Iranian government (Mikdashi 1966, 109). With its major source of revenue

gone, the nationalist government became relatively less attractive to Iranians. In

1953, Mossadegh was deposed in an American-supported coup (Kinzer 2003). The shah was restored to power and cooperation between Iran and Western nations resumed. U.S. and British policies of noncooperation with Iran helped hasten the removal of the nationalist group from power. The United States once again adopted these noncooperative policies toward Iran in 1979 after the shah was deposed in an

Islamic revolution. It is useful to think of the two processes shaping the pattern of international

cooperation in the context of Putnam's (1988) two-level game metaphor. He argued that national leaders negotiate agreements but that these agreements need domestic ratification to be enacted. The group in power determines which agreements can be ratified. The first process, in which the group in power determines what cooperation can be agreed to, is within this genre. The second process completely reverses the

argument. Foreign powers shape ongoing agreements to influence which group attains power (Smith and Hayes 1997).

International Cooperation, Leaders, and Groups

The model examines leader survival in the context of an infinitely repeated game of international cooperation and domestic political competition. Nations 1

and 2 engage in international cooperation, modeled as a prisoner's dilemma. Nation 1 is treated as a unitary actor. Nation 2 is led by a leader who comes from either

Group A or Group B. Leaders are titled according to their group. Leaders are pri marily motivated to keep their jobs. Specifically, in addition to any pay-offs from international cooperation, the incumbent leader receives a pay-off of for each




period he or she retains office. Political competition is modeled using a simple ver sion of the selectorate theory (Bueno de Mesquita et al. 2003), in which the citizens care about the private and public goods that a leader provides as well as any group

specific benefits, the outcome of international cooperation, and the performance of the leader on all other dimensions. This later, catch-all, category is modeled as a

random variable.

In the selectorate model, leaders need to retain the support of a winning coali tion of size W. These supporters are chosen from a pool of potential supporters, of size S, known as the selectorate. Leaders use a combination of private and pub lic goods to reward their supporters. The key insight in this theory of political sur vival is that a leader's policy choices and her ease of survival depend on political institutions. When the coalition size is small, a leader provides her supporters with a high level of rewards by dividing her available resources into private goods for her small number of supporters. In such a circumstance, supporters are

reluctant to defect to a challenger. Should the challenger come to power he might reorganize his coalition of supporters. This could leave a former coalition mem

ber without access to the valuable private rewards. Small coalition systems

engender loyalty. In contrast, when coalition size is large, as it is in democracies,

supporters more readily defect to a challenger. When coalition size is large, pri vate goods are a less effective means of rewarding supporters because resources must be diluted over a large number of supporters. In this case, leaders predomi nately utilize public goods to reward their coalition. Because all citizens receive these benefits whether they are in the coalition or not, coalition members jeopar dize less if they defect and support a challenger. What is more, because the new leader needs to pick a large coalition of supporters, defectors are more likely to be included in future coalitions anyway.

Selectorate theory shows that the ease of political survival increases as coali tion size decreases and selectorate size increases. Selectorate competition is

explicitly modeled in the appendix. This article does not develop selectorate the

ory, but rather uses it as the underlying model of political competition. To

explore the implications of political institutions on international cooperation I use

the results derived from the selectorate model. This allows a concise description of political competition that is grounded in a micro-level theory of political survival.

At the start of each period, the citizens in Nation 2 observe a random shock 0 associated with the incumbent leader's performance. The distribution of 0 is F(x), such that Pr(0 < x) = F(x), where F(x) is continuous and has full support. The citi zens decide whether to retain or depose their leader. Whereas all members of the selectorate might have a say in choosing the leader, the decision that matters is whether or not members of the incumbent's winning coalition remain loyal. Based on the selectorate theory derived in the appendix, a leader from Group A survives in office provided that < A + 7, where Y relates to pay-offs from international




Figure 1

The Prisoner's Dilemma Model of International Cooperation

Nation 1 Cooperate

Don't Cooperate

Nation 2

Cooperate Don't Cooperate

-1 ,R2 + e

*1+X.-1 0,0

Note: Where Ri >0,R2e {RA,RB}, > 0, and e > 0.

cooperation between Nations 1 and 2, to be explored in the following, and 0? is a

threshold derived from the selectorate theory. In particular this threshold is

decreasing in W and increasing in S. This setup allows a simple presentation of the survival incentives. Given the expected pay-off of Y from international coopera tion, Leader A survives with probability F(0A + Y). Given how varies with W and 5, political survival becomes harder as W increases or as S decreases. An ana

logous survival condition applies to Leader B. Nations 1 and 2 interact in each period of the game in a prisoner's dilemma

model of international cooperation. Nation 1 and the leader in Nation 2, who could be either Leader A or Leader B, choose to cooperate (C) or not (~ C). The pay-offs from the game are shown in Figure 1.

If no cooperation occurs, then the pay-offs are normalized to zero. If the nations

cooperate (C, C), then they both gain. In particular, Nation 1 gains R\. All the peo

ple in Nation 2 also gain from cooperation. However, the extent to which they value cooperation depends on group membership. For people from Group A, the rewards from mutual cooperation are R2=Ra- Those from Group receive

R2=R?. There is an incentive to exploit the other side's cooperation. These temp tation pay-offs are R\ + and R2 + e, respectively. As the focus of this article is the ability of different groups to cooperate and Nation l's desire to favor one group over another, Nation l's incentive to cheat is assumed to be small, -> 0.

Nation 1 does not have any direct control over picking the leader in Nation 2.

However, it cares about which group is in control of Nation 2. Nation 1 receives a

pay-off of if Group A rules Nation 2. The pay-off associated with Group is normalized to 0. The pay-off reflects l's like ( >0) or dislike ( <0) of

Group A. This pay-off reflects any preference over groups, be the groups based on

linguistic, religious, ideological, ethnic, or economic divisions. For instance, during the cold war, the United States strongly disliked groups with communist ideology.




The model is an infinitely repeated game. Nation 1 and Leaders A and have a common discount factor . The stage game is as follows:

1. The selectors in Nation 2 observe the random shock associated with the incumbent for

that period, . They then decide whether to retain or depose their leader based on the

voting rule described previously. 2. If deposition occurs, then with probability a new leader is drawn from Group A. The

new leader comes from Group with probability 1? p. This new leader randomly picks W supporters from her group's selectorate to form a coalition.

3. Nation 1 and Leader 2 (be she the incumbent or a new leader) interact internationally, modeled as a choice between C and ~ C in the prisoner's dilemma game.

Domestic Groups and International Cooperation

The model explores how domestic institutions and group membership affect

international interactions through the characterization of stationary subgame per fect equilibria. The stationary condition ensures that players behave the same way in structurally identical situations so that play is not conditioned on arbitrary fac tors such as the time period. As is always the case with infinitely repeated games, there is a profusion of equilibria. I focus on equilibria in which cooperation is

enforced with a simple trigger strategy. Within the prisoner's dilemma the perma nent removal of cooperation, often referred to as the grim trigger strategy, is the harshest punishment available. The equilibria considered thus represent limiting cases as to how much cooperation can be maintained (Fudenberg and Maskin

1986; Osborne 2004, chap. 14).

Noncooperation is always equilibrium behavior in the prisoner's dilemma game. If Nation 1 and Leaders A and play

~ C, then no player can improve his or her welfare by switching to C. This is a well-known and standard result. I label this

equilibrium E0 and use it as the baseline against which to compare other patterns of cooperation. In this baseline case, Leader A survives with probability F(0A ) and

Leader survives with probability F(0^ ).

Mutual Cooperation: El

Provided that both Groups A and value cooperation sufficiently, Nation 1 can

cooperate with both groups in Nation 2 through the threat of reciprocal punishment. This equilibrium, labeled El, examines the most cooperative situation where Nation 1 cooperates equally with both groups. The characterization of the equili brium uses the standard approach of a grim trigger strategy; that is, start out coop

erating and continue to do so unless the other side does not, at which point, never

cooperate again. However, in contrast to the standard unitary approaches, Nation 1




targets its punishment against individual leaders. In this setting Nation 1 restarts

cooperation with Nation 2 once a new leader is elected. McGillivray and Smith

(2008) refer to this as a leader-specific punishment. The threat of losing tenure

keeps leaders from both groups cooperating, so full cooperation is maintained. As is common in infinitely repeated games, a formal statement of the equili

brium strategies is cumbersome. For this reason, formal characterizations are given in the appendix. An informal description conveys the important properties of the

equilibrium without excessive notation. The term cheat indicates that a player plays ~ C; when on the equilibrium path, she should play C. This is a common usage of the term in the description of infinitely repeated prisoner's dilemma games (Keo hane 1984).

Provided that the temptation to cheat, e, is not too large, full cooperation occurs

via the following equilibrium: Nation 1 and the leader in Nation 2, be this A or B,

play C provided that neither the current leader in Nation 2 nor Nation 1 has ever

cheated. If either side has ever cheated then play ~ C. In this equilibrium, Leader

A survives with probability F(0? ) if she has not cheated in the past and survives with probability F(Q? -Ra) if she has previously cheated.

To understand how and why these strategies support cooperation, it is useful to characterize the conditions under which they constitute equilibrium behavior. Con sider the situation as it relates to Leader A. On the equilibrium path, leaders from both groups cooperate. As a result, members of Group A receive the rewards of

cooperation, Ra, provided that their leader (be she A or B) has never cheated. Now

suppose that the incumbent leader is from Group A and that she has previously cheated. Given this cheating, Nation 1 refuses to cooperate with Leader A so every one in Nation 2, and in particular the members of A's winning coalition, miss out on the rewards of cooperation. If A's coalition retains her, then they will receive

Ra fewer rewards than if they depose her, because any new leader will restore

cooperation with Nation 1. Therefore, if Leader A has cheated, then she is less

likely to survive in office as she cannot generate the cooperative rewards that another leader can. In particular, a Leader A who has previously cheated survives with probability F(QA -Ra), while a leader who has never cheated survives in office with probability F(QA ). The off-the-equilibrium path threat of leader removal ensures that leaders do not deviate from the equilibrium path and so cooperation is

maintained.

In the current period, Leader A can improve her pay-off by e if she cheats and

plays ~

C, but if she does so she reduces her prospects of political survival in future

periods and ends her ability to cooperate. Provided that the temptation to cheat, that is e, is not too large, then cooperation is possible. What constitutes "not too large" depends on the size of the group rewards from cooperation (Ra) and political insti tutions and is formally derived in the appendix.

Figure 2 demonstrates the impact of political institutions on the maximum temp tation Leader A can resist before cheating. Figure 3 plots how the probability with




Figure 2 Political Institutions and a Leader's Ability to Cooperate (Full

Cooperation, El)

50 100 150 200

Winning Coalition Size, W

Note: Figure 2 assumes F(x) = 1 -e~\ u(g) =

y/g, v(z) =

y/z, SA = SB = S{= 500, = .8, = .5, = 0,RA =Rb=R\ = 1, = 10,M = 500, = 500, =0.

which a leader survives in office depends on whether or not she has cheated F(0? ) and F(0?

- Ra)- Although the figures are just numerical examples, they show the

underlying incentives. When winning coalition size is small, the incumbent's sup porters are loyal because they receive high levels of private goods under the incum bent they cannot guarantee they will receive under alternative leadership. In the

limit, as coalition size becomes very small, leaders become virtually assured of sur

vival: F(0? -

Ra) -> 1 and F(0? ) -? 1. This is equivalent to treating Nation 2 as a

unitary actor, in which case A's only incentive not to cheat is the loss of future

cooperation. As coalition size increases, and so private goods become less impor tant for rewarding supporters, Leader A's survival in office becomes more tenuous and dependent on delivering cooperation. Although Leader A can improve her immediate pay-off by cheating, she reduces her ability to survive the next period from F(QA ) to F(dA

- RA). As W increases and political institutions become more

inclusive, this difference increases. This means that as leaders become more demo

cratic, if they cheat, then they are increasingly likely to be removed from office. This shift in survival probabilities becomes greater when supporters value coopera tion highly (RA large). Because leaders are assumed to primarily care about staying in office, large coalition leaders can commit to resist the temptation to cheat. This .is seen by the increasing temptation that leaders can resist as coalition size increases. This is the mechanism behind McGillivray and Smith's (2000, 2008)

model of international cooperation through leader-specific punishments.




Figure 3 Leader Survival in the Full Cooperation Equilibrium (?1)

-1-1-1-1-1-1-.-1_ _ _I_ _ _ _ _I_

50 100 150 200

Winning Coalition Size, W

Note: Figure 3 assumes F(x) = 1 -e"*, u(g) =

y/g, v(z) =

y/z, Sa=Sb = S{= 500, = .8, = .5, = 0, RA=RB = R? = 1, = 10, M = 500,/? = 500, , =0.

In very large coalition systems, that is, the right-hand side of Figure 2, the temp tation leaders can resist declines slightly. The argument for the rise in the ability to resist temptation, as explained previously, was that as W increases, F(Q?- Ra) decreases?leaders who cheat are unlikely to survive. However, increases in W also decrease F(QA ), as seen in Figure 3. The risk to tenure from cheating increases as coalition size grows, that is, the gap between F(QA- RA) and F(QA ) widens. How ever the decline in F(QA ) means that the present value of holding office declines as W increases because leaders cannot expect to hold office as long, and so what they jeopardize by cheating (their tenure in office) is worth less.

The full cooperation equilibrium, ?1, demonstrates the maintenance of interna tional cooperation through the threat of reciprocal punishment. It also provides an account of why democratic nations cooperate more than other pairs of nations.

Next, I examine circumstances where Nation 1 cooperates with one group but not the other.

Partial Cooperation, El

Equilibrium E2 considers the case where Nation 1 and Group A cooperate using a trigger strategy to enforce cooperation but Nation 1 and Group do not coop erate. Partial cooperation can arise for one of two reasons. First, one group might




be unable to commit to cooperating because it does not value cooperation suffi

ciently. Second, even if cooperation is possible with both groups, Nation 1 might prefer to cooperate only with Group A to bias the domestic politics in Nation 2 toward its preferred group.

In the fully cooperative equilibrium, El, both Group A and Group cooperate with Nation 1. For this to be equilibrium behavior, both groups need to value long run cooperation sufficiently that it outweighs the short-run benefits of cheating. If one group (B) gains relatively little from international cooperation, then a leader from this group is unable to commit to maintain cooperation and therefore coopera tion cannot take place when this group's leader is in power. In this situation,

Nation 1 can only cooperate with Nation 2 when Group A is in power. The situation of partial cooperation as a result of one group being unable to

commit is more likely to occur in nondemocracies than democracies. As seen in

Figure 2, large coalition leaders are better able to resist the temptation to cheat than are small coalition leaders. Therefore, democrats can maintain cooperation more

effectively than autocrats even if the group they represent gains relatively little from international cooperation.

Full cooperation is not possible if one group does not gain sufficiently from

cooperation. In such a case, only partial cooperation is possible. However, this is not the only reason for partial cooperation. Even under conditions where Nation 1 could cooperate with both groups, namely, the full cooperation equilibrium El

exists, Nation 1 might prefer to cooperate with only one group. By cooperating with only one group, Nation 1 increases the likelihood of leaders from that group remaining in power and reduces the expected tenure of leaders from the other

group.

If Nation 1 cooperates only with leaders from Group A, then Leader A can offer her supporters RA more rewards than can Leader B. This makes A's supporters more loyal because, with probability (1

? p), if they depose their leader, then they

lose the benefits of cooperation. This enhances the survival of Leader A. It also reduces the survival of Leader B. Leader cannot generate the cooperative rewards (/?#), but with probability p, B's supporters would benefit from these rewards if they depose B. This reduces the loyalty of B's coalition.

If Nation 1 prefers Group A to Group B, then selective cooperation with Nation 2 increases the likelihood that its preferred group prevails in Nation 2. Figure 4 illus trates the expected pay-off from full and partial cooperation (that is equilibria El and E2). These pay-offs depend on whether the initial leader is from Group A or B.

When Nation 1 has no preference for one group over another ( = 0, the left side of the graph), full cooperation is the dominant choice. However, as s preference for Group A grows, partial cooperation becomes the preferred choice as 1 is willing to trade off the returns from cooperation to increase the chance of having Group A in power.




Note: Figure 4 assumes ^F(x) = 1 ? e *, u(g) =

y/g, v(z) =

y/z, SA = SB = S\ = 500, = .8, = .5, = 0,/? =/?? = /? = 1, =10, = 500, = 500.

Figure 4 illustrates several interesting features in the trade-off between full and

partial cooperation. The point (in terms of ) at which partial cooperation domi nates full cooperation differs according to whether the current group in charge is A or B. For instance, in the example shown in Figure 4, once > 1.25, Nation 1 pre fers the partial cooperation to full cooperation if it starts with a leader from

Group A. However, if Leader is the incumbent, then Nation 1 receives a lower

pay-off from partial cooperation than full cooperation unless > 2.25. Hence, in the intermediate range where 1.25 < < 2.25, if Nation 1 formulates a policy for

dealing with Nation 2 while it is under the leadership of Group A, Nation 1 may

subsequently regret that policy choice after the ruling group changes. Of course, because the policies are part of a subgame perfect equilibrium, Nation 1 wants to

carry them out. But it might still have ex post regret about its initial choice of

policy. Political institutions in Nation 2 also affect Nation s choice of policy. As win

ning coalition size contracts, leader replacement becomes more difficult. This reduces the attractiveness of a partial cooperation strategy if the incumbent is from

Group B. Although a partial cooperation strategy increases the likelihood of Leader being removed, given a small winning coalition, this turnover probability




is low. In this situation, partial cooperation results in long-run noncooperation between 1 and 2. Unless Nation 1 strongly prefers A to B, the very small chance of

helping depose Leader does not offset the lost opportunities for cooperation. However, when Leader A is in power, formulating a pro-A strategy of partial coop eration is Nation s best policy once it moderately prefers A to B. Nondemocratic institutions and policies developed to promote the interests of a leader from a

favored group can lead to long-term acrimonious relations between nations when leader turnover does eventually occur, as was seen in the case of Iran after 1979.

Partial cooperation was a prevalent feature during the cold war. While the Uni ted States would not cooperate with pro-communist governments, a shift to a pro

Western governing group rapidly reinstated cozy relations. Through such policies, the United States hoped to undermine pro-communist governments and strengthen pro-Western ones. Of course, while a pro-communist government persisted, there was little cooperation.

Pro-A Policies

If Nation 1 strongly prefers Group A to Group B, then it allows leaders from

Group A to cheat. By doing so, Nation 1 increases the benefits Leader A can pro vide relative to Leader B. This shifts the domestic political process in favor of A,

by making it easier for leaders from Group A to survive and undermining leaders from Group . I consider two equilibria in which Nation 1 allows Leader A to cheat in every period. In equilibrium E3, Nation 1 cooperates with Leader via a

trigger strategy. In equilibrium ?4, Nation 1 never cooperates with Leader (plays ~C).

Pro-A policies increase the benefits Leader A can deliver to her supporters. In both E3 and E4, Group A supporters receive the temptation rewards Ra + e when Leader A is in power. Leader delivers less to her supporters. In particular, when

is in power B's supporters receive Rb in equilibrium E3 and 0 in equilibrium E4 from international cooperation. This superior ability of Group A leaders to deliver rewards relative to Group leaders increases the tenure of A and reduces the tenure of B. In equilibrium ?3, Leader A survives with probability

F(0? + e(1 -

)) and Leader survives with probability F(Q^- e ). In ?4, the

corresponding survival probabilities are F(QA +(Ra + e)(1 -

)) and F(0# (#? + e) ). In terms of A's survival, E4>E3, E2>El. Whether A's survival is

higher under equilibrium E2 or E3 depends on the relative size of e and Ra- B's sur

vival under each of these equilibria shows the opposite pattern. Pro-A policies by Nation 1 introduce a bias in favor of Group A leaders.

Figure 5 examines the long-run consequences of Nation s choices by plotting the

long-run proportion of leaders from Group A against the temptation to cheat, e.

Specifically, Figure 5 plots the stationary distribution of a Markov chain where the




Figure 5

Long-run Proportion of Group A Leaders and the Temptation Pay-off for Various Equilibria

1.0

? 0.8 (0

c 0.6 o

o

o 0.4 ?. c 3

6) 0.2

Pro-A No Cooperation, E4_- -

^ ^

Pro-A with Cooperation, E3

Partial Cooperation, E2

Full Cooperation, E1

1 2 3

Temptation to Cheat, e

Note: Figure 5 assumes F(x)= 1 -e_JC, u(g) =

y/g, v(z) =

y/z, SA = SB = Si= 500, = .8, = .5, = 0, /? =/?0=/? = 1, =10, =500, = 500.

transition probabilities come from the probability of leader retention. For example, in the case of El, let a be the long-run proportion of leaders from Group A: a = oc(F(eA*) + (1

- F(Q*))p) + (1

- oc)(l

- F(G *))p. The flat solid line at 0.5 indi

cates that in the long run with full cooperation, El (or the noncooperative base case

E0), half the leaders will come from Group A and half will come from Group B. In this equilibrium, Nation 1 cooperates equally with both groups. In equilibrium E2,

Nation 1 cooperates only with Group A leaders, which biases political competition in favor of A. The long-run proportion of Group A leaders in this equilibrium is shown by the second flat line (long dashes) at about 0.73. The pro-A equilibria E3

(medium-length dashes) and E4 (short dashes) can result in even higher long-run proportions of Group A leaders, particularly when the rewards from cheating, e, are

large. Pro-A policies enable Nation 1 to promote its preferred group. When deciding which policy to pursue, Nation 1 trades off between influencing

which group is politically dominant and maximizing cooperation. Obviously, the more Nation 1 favors Group A, then the more attractive pro-A policies become.

However, Nation 1 needs to consider not just the long-term consequences, which are shown in Figure 5, but also the speed with which these biases are felt. Small

winning coalition size engenders a norm of loyalty. In such systems, leader




turnover can be very slow. While a pro-A policy may create a long-term bias in favor of Group A leaders, in small coalition systems it may take a long time before a Group leader is ousted. This makes pro-A policies less attractive against lea ders from small coalition systems. Pro-A policies are therefore more likely to be

adopted against large coalition systems. Only if Nation 1 strongly prefers Group A to Group does it adopt pro-A policies against a small coalitions system, and if Leader is the incumbent, then the expected result is long-term rancorous relations between the two nations.

Nation s ability to influence political competition in Nation 2 depends on 2' s

institutions. This has implications for democratization. When Nation s preferred group is in power, 1 has relatively little incentive to promote democratization.

Doing so would make it more likely that its preferred group is deposed. In contrast, when Group is in power and 1 strongly prefers Group A, Nation 1 wants to

encourage democratization. Nation 1 is selective in where and when it promotes and encourages democratization (Bueno de Mesquita and Downs 2006; Hermann and Kegley 1998; Peceny 1999). The model sees no contradiction in propping up friendly dictators in one case and promoting revolution and protest in another. Nation 1 gains most from democratizing Nation 2 when it is antagonistic toward the current leadership and there is a significant group in Nation 2 with which it shares common interests. In contrast, Nation 1 should discourage democratization when Nation 2 is ruled by those from its preferred group.

Discussion

Relations between states vary enormously. This variation is both cross-sectional and across time. The theory accounts for this variation by integrating arguments about leader survival, domestic politics, and international cooperation. Extant argu ments within the liberal paradigm show how reciprocal punishments can support international cooperation. Yet, this is an existence result: it shows that cooperation can be maintained. It does not elucidate why cooperation occurs between some

nations and not others. The theory derives predictions about the relationship between leader turnover and interstate cooperation and the moderating impact of

political institutions. The theory argues that nations are composed of different political groups, and

this can jeopardize international cooperation in two ways. First, groups gain differ

entially from international cooperation. Leaders from groups that gain little from

cooperation cannot commit to cooperate. Second, states discriminate between the

groups in other nations. If Nation 1 prefers Group A to be in power in Nation 2 rather than Group B, then Nation 1 may selectively cooperate so as to allow leaders from Group A to deliver greater rewards to their supporters than can Group lea ders. Such discrimination biases the political competition within Nation 2 in favor




of leaders from Group A. If Nation s preference for Group A over Group is

really strong, then Nation 1 might shift political competition even more strongly in

A's favor by systematically allowing Group A leaders to cheat without retaliation. When leader change results in a different group being represented, the level of

cooperation between states may change. McGillivray and Smith (2004, 2008)

investigate trade flows and sovereign debt, and McGillivray and Stam (2004) examine economic sanctions. They find evidence that changes in each of these international interactions is associated with leader change. Yet, their studies do not

identify whether all leadership changes have these effects or whether the observed

effect occurs only when the group of the leader changes, as suggested by this arti cle. Although no systematic empirical tests have examined this question, there is

evidence to suggest the latter. For instance, the level of foreign aid a nation

receives and the terms and conditions of IMF and World Bank programs are all

strongly influenced by friendliness with the United States (e.g., Vreeland 2005).

During the cold war, the United States was particularly likely to condition its rela

tions with a state depending on the pro- or anti-communist leanings of its leaders. This article presents a simple model of international cooperation that accounts

for the huge variation in interstate relations. International cooperation cannot be

divorced from the survival incentives of political leaders and the nature of domestic

political competition. Cooperation between nations is uneven and depends on

which groups are in political ascendency. International relations are driven by domestic political competition.

Appendix

The main text dealt with leader retention as a probabilistic voting problem. Here I pro vide micro-foundations for this decision making by using a simple version of the selectorate model. Let u(g) and v(z) represent a citizen's utility functions for receiving public (g) and

private (z) goods. Both functions are smooth continuous concave functions normalized such

that v(0) = 0. Suppose the price of public goods is and the effective price of private goods is W, the number of people who receive them. If a leader has M resources, then the leader

can do no better than maximize the welfare of her coalition. This program,

u(g *) -f v(z *) = maxg, z u{g) + v(z) subject to the budget constraint M > pg + Wz, is well characterized (Bueno de Mesquita et al. 2003). The level of public goods is increasing in coalition size; increasing coalition size causes a contraction in the provision of private goods.

The numerical examples assume u(g) = ,/g and v(z) = y/z, which implies g* =Mp^+p) and z* = Mw^+py

In addition to these private and public goods, citizens in Nation 2

receive the pay-off if their leader is from their group. Initially ignore the pay-offs from the prisoner's dilemma and suppose Leader A is in

office and the shock associated with this leader's performance is . If Leader A's coalition retains her, then their pay-off is u(g* ) + v(z

* ) +

? . This relates to the optimal provision of public and private goods plus the group good ( ) minus the leader's liability on all other




issues ( ). Alternatively, members of the coalition could defect and depose the incumbent. If

they do so, then with probability the next leader is also drawn from Group A, in which case the defectors receive the group good. Conditional on a Group A leader attaining power, Group A selectors also have aW/SA chance of being included in the new coalition and thus receive private goods, where SA is the number of selectors in Group A. If a Group leader attains power, which happens with probability 1

- p, then Group A selectors receive neither

group goods nor private goods. Therefore, the expected value of deposing Leader A is

|^*) + ( *) + ) + (1-^^ A comparison of these pay-offs shows that Leader A's coalition remains loyal provided

that 9<9A =v(z*)(l -

pjj) + a(l

- p). An analogous calculation shows that Leader

survives if < Q*B

= v(z*)(1- (1 ?

p)J?) + . Leader A survives with probability F(9A).

Because *, the optimal level of private goods, is decreasing in W, Leader A's survival is

decreasing in W and and increasing in SA and : < 0, ^ < 0, > 0, and ^

> 0.

To formally characterize the equilibria, I define Hi and Hi as the previous history of play for Nation 1 and the current leader in Nation 2. Because I restrict attention to simple trigger strategies, the only relevant aspect of the current history is whether the player previously cheated. Therefore, let H\ = if Nation 1 has previously cheated. If Nation 1 has never chea

ted, then we say it is honest, H\=h. Use analogous notation for 2. What it means to cheat is

specified for each equilibrium.

Noncooperation: E0

All players play ~ C and Leaders A and survive with probability F(9A ) and F(9g ). Let ZA0 and ZBo represent the expected value of playing the game for Leaders A and B,

respectively. ZAo = F(9A )) + A0), which represents the probability of surviving (F(9A )) multiplied by the value of office holding in the current period ( ) and the discounted value

of playing the game starting in the next period A ? Therefore, ZAo = 7^^*^ Similarly, l-?F(VA)

F{Q * )

ZBo= . Let ? AO represent Nation l's pay-off from playing the game starting with 1 Or(V?) Leader A in power and Qbo be the associated pay-off if Leader rules Nation 2:

QA0 = F(Q*a)(g? + ?A0) + (1 -

^( ;))( ( + ? ) + (1 -

)(0 + ? )). This expres sion deserves explanation. The first term, (F(9a)(gi -f ?^ )), describes the probability Leader A survives in which case Nation 1 get the benefit from having Group A in

power and the discounted benefit of the game starting in the next period with Leader A. The second term captures the eventuality in which the leader does not survive, which occurs

with probability (1 ?

F(9A)). In this case, with probability the next leader is also from

Group A and with probability 1 - a Group leader attains power. The analogous expres sion for Nation l's value from playing the game with a leader from Group is

Qbo = F(9*) ??0 + (1 -

F(9*))( ( + ?A0) + (1 -

) ?? )? Solving these two expres . ?0 ? ,jc n ai(-5f(e*)p + p + (l-5)(l-p)f(e^)) _A ^ ^ -^ !)) sions yields ?A0 =

(1_5)(5(gp_1)F(e;)_5pF(e;) + ̂ and Qbo =

w^^-Wj + iy The




base case equilibrium is characterized by the survival thresholds ( A, ^), the benefits to Leaders A and (ZAq, Zbo), and Nation s pay-off against each leader (QAq, Qm)

If Nation 1 plays C instead of ~ C mmas then it reduces its payoff by 1 in the current

period without affecting future play. Therefore, switching strategies is never optimal. An

analogous argument applies to Leaders A and B.

El: Full Cooperation Start by specifying what it means to cheat. All nations start with honest reputations. If

Nation 1 plays ~C when Leader 2 has an honest reputation, then s reputation becomes

permanently dishonest, H\ = . If Leader 2 plays ~C when Nation s history is honest

(H\ = h), then Leader 2's reputation becomes dishonest (H2 = ) until such time as the lea der is replaced.

Proposition: Equilibrium El. If e < ^ = ?(ZAh\ -

ZAy\) and e < X?i = ^(Z?h\ ? # ),

where ^= iVe*)

' z^1 = i-8Ae;-^)'

Z?hl= i-me*B)

' m? ^ =

ey? *_R dW B then the following strategy is a subgame perfect equilibrium: if Hi = or H2 = l-0F(?l-RB)' then Leader A, Leader B, and Nation 1 all play

~ C (i.e., play as in equilibrium EO); i?H\=h and H2 = h, then Nation 1, Leader A, and Leader all play C.

Proof. I characterize the expected value of playing the game and prove that the aforemen tioned strategy profile is a subgame perfect equilibrium. I commence with an examination of the selectors' deposition decision. If Nation 1 is dishonest, H\ = , then the analysis is as per equilibrium EO. Therefore, suppose Nation 1 is honest: H\=h. Suppose Leader A has an honest reputation, H2 = h. Under this scenario, Leader A plays C. For the selectors in her coalition the value of retaining her is u(g* ) 4- v(z* ) + 4- RA

- . If the selectors depose

her, then their expected pay-off is ?(#*) + pj^v(z*) + + RA. The comparison of the

relative values from keeping and deposing A implies that the Group A selectors in the win

ning coalition depose Leader A if > v(z * )(1

? ^ ) 4- (1 ? ) = A.

If Leader A has previously cheated, then the value of retaining her is less, as cooperation

does not occur in the prisoner's dilemma: ?(g*)-f v(z*) + ? . The expected value of

deposing her is u(g * ) + (

* ) + + RA. Therefore, selectors depose a dishonest Leader

A if > v(z * )(1

? ) + (1

- ) = A ? Ra- The analysis is analogous for Leader B.

Having established how reputation affects survival, next I calculate the continuation

values. For Leader A with an honest reputation the expected value of playing the game is

ZAhi = F(0A )( +-\-bZAh\). The expected value of playing with a dishonest reputation 7 EYQ * D A / 7 \ TV, ? 7 F(Q*))W + RA) F(?* -*A) is ZAyl

= F(0A

- Ra)?? + ). Therefore, ZAhx = > zAyi

= ^^?-r^

F(Q )) ~\~ R?} The continuation values for Leader are similarly calculated: Zbm =

/grrq*? > 1? oF(d? )




Continuation values for Nation 1. Suppose the initial Leader 2 is honest and from Group

A:?am = F(e; )( + J?i + bQAhX) + (1

- F(Q* )) ( + ?, + ?A ) + (1

- ))

(1 ?

p)(#i + ?? )? Nation l's continuation value associated with Leader is

Qbm = F(Q*B))Ri + ? ) + (1 -

E( ;? ( +?i + ? A ) + (1 - ^?(l

- )(/? +

??/, ). Solving these expressions yields ? a = ? + ?ao and QBhl = ^ + ? ? ?

Having calculated the continuation values, I now show there are no utility improving shifts in strategy for any player. In histories with dishonesty (Hi = or Hi = ), no player cooperates. In these situations, playing C is always dominated. Suppose honest histories

(#i = h and Hi = h). If Leader A cooperates, then her expected pay-off is RA + 4- A/ .

However, if Leader A cheats, then her pay-off is RA + e 4- + hZAl\. Thus, Leader A coop erates provided that e < A\ = ?(ZAhi

- Ayl)- Similarly, Leader cooperates provided that

e< ?1 = ( ? -

? ).

We now consider Nation l's incentives against Leader A. If Nation 1 plays C, then its

expected pay-off is R\ + ?A/, ? Alternatively, if Nation 1 "cheats" and plays ~C, then

although 1 gains the additional benefit of cheating, it loses its honest reputation such that in all future periods no cooperation occurs (which has a continuation value of ?A )? Nation l's pay-off under this contingency is R\ + + ?^ - A comparison of these pay-offs reveals that 1 only cheats if > bQAn\

- ?^ =

fz?- Because is small ( -> 0), this condition

always holds. Hence El is a Subgame Perfect Equilibrium (SPE) under the specified condi tions. QED.

El: Partial Cooperation I start by specifying what it means to cheat. All nations start with honest reputations. If

Nation 1 plays ~C when Leader 2 is from Group A and has an honest reputation, then l's

reputation becomes permanently dishonest, H\ = . If Leader A plays ~C when Nation l's

history is honest (Hi = h), then Leader A's reputation becomes dishonest until such time as

the leader is replaced. Leader B's history will be irrelevant.

Proposition E2. If e < A2 ? ?(ZAh2 - A 2) and QAhi > Qao + x/o, where

- i-eF(e;+*A(i-p))(

+rax zw -

i-ew;-*AP) ' Qahi "

(Rl+ol)(-?F(Q*B-pRB)p+p + (l-m-p)F^*A +*aQ-P))) d q

_ ?1 (~^*B)P + + (l-8)(l-p)F(9;)) (1-?)(?(p-1)F(0* +/?A(l-p))-?pF(0*-ptfB) + l)

' Â0 (1-?)(?(p-1)F(9* )-?pF(G* )+1)

'

then the following strategies are subgame perfect equilibrium. If Hi=h and Hi = h and Leader A rules Nation 2, then Nation 1 plays C; otherwise

Nation 1 plays ~C. Leader A plays C if Hx =h and Hi ? h\ otherwise, Leader A plays ~ C. Leader plays

~ C.

Proof. I start by calculating the selectorate's deposition decisions if Nation 1 is honest, Hi=h. If selectors in A retain an honest Leader A, their pay-off is

u(g*) + v(z*) + <J + RA ? . If they depose Leader A then their expected pay-off is

"(#*) + P^"ufe*) + + â? Note that following deposition selectors only obtain the

rewards of cooperation if a Group A leader is the successor, because Nation 1 does not coop erate with Group leaders. A comparison of these values indicates that Group A selectors in




the winning coalition depose Leader A if > t?(z*)(l -

pjj) + (1

~ P)+#a(1

- P) =

A + RA(l -

)? If Leader A is dishonest then deposition occurs if > v(z*)(l -

pjj) +

G(l-p)-RAp= ; -RAp. Relative to the base case or the full cooperation equilibrium, Group selectors in Leader

B's coalition are encouraged to dispose Leader because leaders from Group fail to deli ver the cooperative goods that Group A leaders do. If the coalition retains Leader B, then their pay-off is u(g*) + ( *) +

? . If they depose Leader B, then their pay-off is

"(#*) + (! -

p)JjKz*) + (l

- ) + ##. Therefore, deposition occurs if > ( *)(1

(1 -

p)^)-f -

/?5 = ? -

pR?. Note this deposition does not depend on Leader B's

honesty because 1 never cooperates with B.

Next, calculate the continuation values for each leader (assuming H\ = h). Let ZAu2

be Leader A's value for playing the game given an honest reputation: ZAya ?

F(0A + RA(l -

))( + /?A + A 2). If Leader A has previously cheated (H2 = y), ZAy2 = F(QA

? RAp)C? + bZAy2). Leader B's expected value for game does not depend

on her honesty because 1 and never cooperate: Zbhi = F(Q*B -

/?#)( 4? *

? )- Sol

Ving these equation yields ZAh2 = ( + RA). ZAy2 =

,^^ , and

Zbhi? Ffj?7*RB\ If H\ ?h, then Nation s continuation values for playing with l-oF(QB -pRB)

an honest A and are QAh2 = (1_S)(5(p_f)F(e; +it,(1.p)Mpf(9;-^)+1)

= ii^tip-^li^Z?ml-îf

resPectively- Given these Preliminaries, I

now show there are no alternative strategies that are utility improving. Note that if both sides are playing ~C, gaining the sucker's pay-off cannot be an improvement. There

fore, the proof requires showing Leader A does not want to cheat Nation 1 and vice versa. Given honest histories, if Leader A plays C, then her pay-off is 4- RA 4- ^.

Alternatively, if she cheats, then her pay-off is 4- RA 4- e 4- o*ZAy2. Because e < A2 =

?(Za?2 -

Ayl), Leader A cannot improve her pay-off by cheating. If Nation 1 plays C

against an honest Leader A, then its pay-off is R\ + b*QAh2> Alternatively, if Nation 1

cheats, then its pay-off is RA 4- 4- ?<2ao- Hence, provided QAh2 > QAq 4- / , Nation 1 does not cheat. Hence, E2 is a SPE.

E3: Pro-A cooperation

I start by defining what cheating means. Nations start with honest reputations. Nation 1

becomes dishonest if it plays ~ C against Leader when Leader has an honest reputation.

Leader is initially honest but becomes dishonest if she plays ~ C against an honest Nation 1.

Proposition: Equilibrium E3: Pro-A cooperation. If e < ? = 0Z?h3 ~

# 3,

Qah3 > ? + Gao , and Qbk? > Qbo + / , where Zm = ( !^]%e)) (rb + ).

F(Q*-pB-RB) w ^(p-l)-^! + (?-l)(CTl-l))F(e/ + e(1- ))( -1) -Tz^r*-? , \?AH3 = ,? .....???,? *?:?-?? ^?. *-??

(?-?F(Q* -pe-RB)) ' Âm

(?-l)(?(P~l)F(QA* + e(?-p))-?pF(Q* - e) + 1)

Q?h3 = ?i(p-l) +

tfi?F(9^_+ e(1- ))(1- ) + - + (* ( -1) + ai-l)F(6fi*

(?-l)(?(p-l)F(9A + ?(l-p))-?pF(e? - e) + 1)




n4n = ^(-8F(9;)p + p + (l-5)(l-p)F(9;)) = _paiO-Ffl,* )) Â0 (1-?)(?(p-1)F(9A* )-5pF(9?* ) + 1)

' (1-?)(?(p-1)F(9A* )-?pF(9?* ) + 1)'

the following strategies are a subgame perfect equilibrium. Leader A plays

~ C. Leader plays C if H\ = h and H2 = h and plays ~ C otherwise. If

Nation 1 is dishonest (H\ ? ), then Nation 1 plays ~ C. If Nation 1 is honest (H\ = /i), then

Nation 1 plays C against Leader A, plays C against an honest Leader B, and plays ~ C

against a dishonest Leader B.

Proof. If H\ = , then the analysis is as per EO. Consider the situation where H\=h. The

pay-offs for Leader A's coalition from retaining and deposing A are

u(g*) + v(z*) + + Ra +e - and u(g*) + pj^v(z*)

+ -hRA. Therefore, A's coali tion retains her provided that < A + e(1

? ). The comparable thresholds for an honest

and dishonest Leader are < ? ? e and < ?

? e ? RB. The continuation value for Leader A is ZAh3 ? ?Ff~X^1 P))?(Ra + e + ). For an

(l-?F(9A + e(1- ))) #

honest and dishonest Leader B, the continuation values are Zgh3= ,? Â**^ ? + ) (l-0F(9?

- e))

j ? F(9*-ps-??) w ^

^=(,_ ,( ?_. )) ?

The continuation values for Nation 1 (given H\=h ) are Qah? = F(Q? +e(1

? ))

( - 1 + , + BQAH?) + (1

- FQ'A + e(1

- )))) )

- 1 + + ?QAm) +(1 - , +

??A3)) and QBh? = F(%*B -

e)(1 + ? ,,3) + (1 -

F(9B -

e))( (-1+Cl+ ?A 3) + , \i d ,5 ? U- u ( -1)-(? +( ~1)( ,-1)) ( *+e(1- ))( -1) (1- )(*,+ ? 3)), which y.elds ? 3 =

(s_1)(g(p_1)F(e>?(1_p))_Sp%>_pe)+1) and

g?3=*(P-?+*?ffi;^ I now show that no ( -1)( ( -1) ( A +e(1- ))- ( ?- e)+1)

player has a utility improving defection. Leader A gains the largest possible pay-off and so has no better strategy. Given honest reputations, Leader obtains pay-offs of RB + ?ZBh3 from C and RB + e + ? 3 from ~ C. Provided e < = ^3 ? ? 3, Leader does not defect. Against Leader A, if Nation 1 plays C, then his pay-off is ? l + -\-?QAh3'-> if

Nation 1 plays ~C, his pay-off is + ?Qao- Hence, provided that Qah3 > + ?ao, 1 allows A to "cheat." Against Leader B, if Nation 1 plays C, then his pay-off is #i + ??/^; if Nation 1 plays ~C, his pay-off is Ri+% + $QBo- Hence, provided that

Q?h3 > Qbo + / , then 1 cooperates. Hence, under the conditions specified, E3 is a SPE.

E4: Pro-A, No Cooperation

In this equilibrium, Nation 1 plays C against Leader A and ~ C against Leader B. Nation 1 starts honest but becomes dishonest (H\=y) if it plays

~ C against Leader A. The history for Nation 2 does not affect play.

Proposition: E4: Pro-A, no cooperation. If Qaha > \ + ?ao? where Qaha =

(l-a1)(5F(9;-p(/?fl+e))p-p-(l-6)(l-p)F(9A+(/gA+?)(l-p))) gl(-5F(9* )p+p+(l- 5)(1 -p)F(9* ))

(l-6X5(p-l)F(9A+(i?A+EXl-p))-6pF(9;-p(?j,+e))+l) Â0

(l-6X6(p-l)F(9*)-6pF(9j)+l) '

then the following strategies are a subgame perfect equilibrium.




If Hi =h, then Nation 1 plays C against Leader A; otherwise, Nation 1 plays ~C. Lea

ders A and play ~ C.

Proof. If Nation 1 has previously cheated (which in this case means played ~ C against

Leader A), then play is as per EO, which has already been characterized. Suppose Hx=h. First

consider survival. The pay-offs for Leader A's coalition if they retain or depose her are

u(g*) + v(z*) + <J + RA + e - and ?(#*) + |^- ( *) + + p(RA + e). Hence, they

depose her if > A -h (RA + e)(1 ?

). The pay-offs for Leader B's coalition if they retain or

depose her are w(g*) + u(z*) + a- and u(g*) + (l -

p)f^v(z*) + (1- ) +

p(RB + e). Therefore, deposition occurs if > Q*B -

p(RB + e). The continuation values for a > 7 F(9*+(/?A+e)(1- ) + /?A+e) ? Fidi-?>(Rb + e))( )

Leaders A and are ZAm = / SEv, , /p , ^

* and ZBHA

-

l-?F(F(QA +(/? +e)(1- ))) Dn*

1-5F(F(0? -p(RB + e)))

The continuation values for Nation 1 against A and are QAha = F(QA + (Ra + e)(1 ?

))

(-1 + 1+ ? ) + (1-^( A+^^ and

QBHA=FQB-rtRB+*))&QBH4+(l^

which solve to the values to Qah4J*-?**wW*b^^^ and ÂHA (l-?)(?(p-l)F(0A+(/?A+8)(l-p))-?pF(0g-p(/?0+e))+l)

miU

p(l-CTl)(F(0*-p(/??+8))-l) Qbha=-*-?

(l-5X6(p-l)F(eA+(J?A+e)(l-p))-5pF(eB-p(i?e+e))+l) I now examine conditions to ensure no player benefits from a shift in strategy. Leader A

has not utility improving strategy as she obtains the maximum pay-off. If Leader shifts to

playing C, then she receives the sucker's pay-off of ?1, which reduces her pay-off. Against

A, if Nation 1 plays C, then its pay-off is ? 1 4- + $QAha\ if it plays

~ C, then it receives + ?<2ao- Hence, 1 plays C provided that QAha > I + Qao- Against B, if 1 plays C, its

pay-off is ?1 + ?QBHa'-> if 1 plays ~

C, its pay-off is ?QBha- Therefore, Nation 1 prefers to

play ~ C. Hence, under the QAha > | + QAo, E4 is a SPE.

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Political Groups, Leader Change, and the Pattern of International Cooperation