Nonseparable Preferences, Issue Linkage, and Economic Sanctions

Nonseparable Preferences, Issue Linkage, and Economic Sanctions Dean Lacy Ohio State University Emerson M. S. Niou Duke University Presented at the Annual Meeting of the American Political Science Association, Boston, MA, September 3-6, 1998.

Nonseparable Preferences, Issue Linkage, and Economic Sanctions Abstract Studies of issue linkage, economic sanctions, and military coercion rarely overlap even though cases of economic sanctions and military coercion are, by definition, cases of issue linkage. The existing literature on issue linkage and economic sanctions examines only cases where both sides in a dispute have separable preferences for the issues under dispute. This paper expands the current literature by introducing two innovations: states in a dispute may have nonseparable preferences for the issues under dispute, and they may not know the preferences of their opponent. Specifically, we develop a game of economic sanctions in which a player does not know whether its opponent has separable or nonseparable preferences. We derive the conditions under which coercer states will choose to impose sanctions on their opponents, and under which target states will choose to capitulate to or resist the demands of the coercer

In a world of growing interdependency among nations, international disputes often involve multiple issues. During the Gulf War, Iraq attempted to link withdrawal of its troops from Kuwait to the resolution of the Palestinian conflict with Israel. United States policymakers have linked China s Most Favored Nation (MFN) trade status to improvements in China s human rights record. Countries supporting the United Nations embargo against Iraq have linked trade with Iraq to Iraqi compliance with U.N. weapons restrictions. These are but a few examples of the growing interdependency among the issues that arise in international disputes. The intertwining of issues in disputes is known in the literature on international relations as issue linkage. A case of issue linkage occurs when one party in a dispute introduces a new issue into the dispute, demanding that the issues be resolved together. Existing studies of issue linkage focus on cases where the states in a dispute have separable preferences for the issues under dispute. 1 When an actor (state or individual policymaker) has separable preferences, her preference for the outcome of one issue is independent of the outcome of all other issues. Often this assumption is unrealistic since a disputant s preference on one issue may depend on the outcome on other issues. For example, in cases of economic sanctions or military coercion, the coercer threatens to use economic sanctions or military means for political purposes. If the target country believes that the coercer has separable preferences, issue linkage will not work because if 1 The preferences of states or other collectives may be described as separable or nonseparable only if the collective has a transitive social ordering over the possible outcomes. While individual preferences are usually transitive, collective preferences often are not. When we speak of the preferences of a state, we assume that the actors in the state have generated a transitive ordering of the outcomes, or that the preferences of a unitary leader define the state s preferences. 1

the target country refuses to comply with the coercer s demand, it is not in the coercer s interests to carry out the sanctions. But if the target country believes that the coercer has nonseparable preferences -- the coercer prefers the outcome (concession, no sanctions) to (no concession, sanctions) to (no concession, no sanctions) to (concession, sanctions) -- the target country should concede to the coercer s demands if it does not consider its political objective to be worth the economic costs. We develop a game-theoretic model of disputes on multiple issues where disputants may have either separable or nonseparable preferences. The key feature of the model is that states have incomplete information about each other s preferences. Specifically, states do not know whether their opponent s preferences are separable or nonseparable. Our model provides a general and unifying framework for understanding diverse but related phenomena in the literature on international conflict: issue linkage, economic sanctions, and military coercion. We derive predictions about the outcome of strategic interaction between different types of disputants, showing that a typology of disputes based on the preferences of the actors in the dispute implies many of the typologies of issue linkage common in the literature. The Problem of Issue Linkage The large literature on issue linkage in international relations demonstrates that issue linkage will be successful in a dispute when two parties weigh the issues differently (Axelrod and Keohane 1986; Haas 1980; Keohane 1984; Keohane and Nye 1977; Li 1993; McGinnis 1986; Morgan 1990, 1994; Morrow 1986, 1992; Sebenius 1983; Stein 1980; Tollison and Willett 1979). When one nation cares most about one issue while the 2

other nation cares most about another issue, the two nations will trade concessions to achieve a mutually beneficial outcome. Conventional wisdom on issue linkage tells a story like this: Suppose a dispute involves two issues, each of which can be resolved either {0} or {1}. The possible outcomes of the two issues, taken together, are (0,0), (1,0), (0,1), and (1,1), hereafter 00, 10, 01, and 11, respectively. Suppose that Nation A most prefers outcome 10, with 11 second in its preference ranking. Nation B most prefers outcome 01, with 11 second. If the two nations weigh each issue differently-- say that Nation A cares most about the first issue while Nation B cares most about the second-- then the two nations can make concessions on the issue that matters least to them in order to gain concessions on the issue that matters most. The outcome of the negotiation would be 11. Morrow (1986) and Morgan (1990, 1994) use a spatial model to describe the preferences of actors involved in a dispute where issues become linked. Morgan demonstrates that when the disputants have different salience weights over the two issues, a Pareto optimal set of outcomes is created. The problem for the disputants is to pick an outcome from the Pareto set. Morgan s model assumes that all disputants have separable preferences for the issues in the dispute: the outcome of one issue has no impact on a disputant s induced preference on other issues. The theoretical literature on issue linkage suggests that linkage always opens room for Pareto improvement over the status quo. Any dispute that involves issue linkage should be resolved peacefully. Empirically, however, issue linkage often fails to generate peaceful resolutions to conflicts. James Morrow has observed that after reading the literature on issue linkage, One may wonder then why war cannot always be avoided 3

through some linkage deal (1992:153). Morrow s answer is that a nation proposing issue linkage may be seen as weak in negotiations. This may be the case under some circumstances, such as when Iraq attempted to link its withdrawal from Kuwait to resolution of the Palestinian problem in Israel. Several scholars have tried to explain the success and failure of issue linkage by developing typologies of issue linkage. The goal of this research has been to classify different forms of issue linkage according the issues involved or the military and economic resources of the disputants. Haas (1980) classifies linkages as tactical, fragmented, or substantive. Li (1993) defines linkages as substantive, symbolic, or transcendent. Both of these typologies rely on differences in the issues under dispute rather than on differences in the preferences of the disputants. We believe that differences in the issues under dispute are important to the outcome of issue linkage only to the extent that different issues may be associated with different preferences held by the states in a dispute. Types of issues are but a proxy for types of preferences. Tollison and Willett (1979) distinguish between positive sum linkage and negative sum linkage. They suggest that situations of issue linkage differ in the underlying preferences of the actors involved in the dispute. To understand the likely outcome of a dispute, researchers must understand what the actors want. However, their typology classifies linkage situations based on the ex post outcome of the dispute rather than on ex ante factors that may determine the outcome of the dispute. Furthermore, Tollison and Willett examine only positive sum linkages, which assumes that issue linkage is Pareto improving. They do not examine negative sum linkages, arguing: we would not expect negative-sum agreements to be quantitatively important in the two-person case since they are irrational for at least one negotiator. 4

although, of course, the negotiator could be coerced into such a move through threats. While such threat consideration can be quite important in some negotiations, they lie beyond the scope of our analysis. (p. 430) When actors have incomplete information about each other s preferences particularly when they do not know if each other s preferences are separable or not then issue linkage may result in Pareto inferior outcomes. Oye (1979) distinguishes between blackmailing and backscratching linkages, a distinction that arises from the preferences of the disputants. According to Oye, The distinction hinges on the interest of the linker in the threatened or promised action. In backscratching, the linker is requesting compensation for refraining from actions that are in his best interest. In blackmailing, the linker is requesting compensation for refraining from actions that are not in his best interest (1979:14) The distinction is similar to Tollison and Willett s negative sum versus positive sum linkages, since, like negative-sum linkages, blackmailing linkages appear to be based on non-credible threats. However, if the blackmailer knows that he will interact with the target state in the future, it may be reasonable to suffer short-term losses in order to secure long-term gains. Tollison and Willet (1979), Oye (1979), Haas (1980), and Li (1993) all recognize that issue linkage is often strategic. Nations may put seemingly unrelated issues on the bargaining table in order to change the terms of the debate over a central issue. To understand issue linkage, one must understand the underlying preferences of the players in a bargaining game. We propose a new typology of issue linkage based on the preferences of the actors in the dispute. By developing a typology of issue linkage based on variations in the preferences of the actors in the dispute, we provide a general framework for the study 5

of issue linkage. Our framework applies to general cases of issue linkage and to specific forms of issue linkage, such as economic sanctions and military coercion. The framework we develop relies on three assumptions about issue linkage. (1) Cases of issue linkage involve a dispute between at least two actors over at least two issues. (2) The preferences of the actors in a dispute are defined over the outcome of the set of issues. Actors preferences over a set of issues may be separable or nonseparable. (3) A situation of issue linkage implies a game between two (or possibly more) players. Players are uncertain of each other s preferences for the outcomes of the game. Assumption 1 is trivially true since the issue linkage, by definition, involves at least two issues. Assumption 2 and 3 bear some discussion. Separable and Nonseparable Preferences When a dispute involves two or more issues, an actor s preferences should be defined not over each issue separately, but over the combination of outcomes of the issues. Researchers often assume that the preferences of actors are separable, or defined over each issue independent of the outcome of other issues. Separability of preferences is a restrictive assumption that is often not valid empirically. To define separable and nonseparable preferences, suppose that an actor can define an asymmetric and negatively transitive preference ordering over all n-tuples of outcomes, where n indexes the issues. We denote by x k the outcome on any issue k, X is 6

an n-tuple of outcomes, and X is the set of all n-tuples of outcomes. X -k = X \ x k, which is an n-1-tuple of outcomes on all issues except k. Y -k = X \ x k, Y X. An actor s preferences are separable if and only if : ( x, X ) f ( x, X ) and( x, Y ) f ( x, Y k. k k i k k k k i k k ) An actor s preferences are nonseparable if and only if for some k there exists an X and Y such that: ( xk, X k ) f i ( xk, X k ) and( xk, Y k ) f i ( xk, Y k ). To illustrate, suppose that an actor s preferences are defined over two issues (n=2), each having a binary outcome (m=2), 0 or 1. There are m n possible n-tuples of outcomes. In the case of two binary issues, there are four possible outcomes. An actor can define a fully ordered preference relation across the four outcomes in 4! =24 possible ways. Only 8 of the 24 possible preference rankings are separable, as Table 1 shows. In the case of 2 issues, all separable rankings are also lexicographic, and vice-versa. For two issues, a necessary and sufficient condition for preferences to be separable is that the top-ranked outcome must be the inverse of the bottom-ranked outcome. With three or more issues, all lexicographic rankings are separable, but not all separable rankings are lexicographic. With three issues involving binary outcomes, 8 different outcomes are possible, producing 8!=40,320 different possible strict preference orderings, only 384 of which 7

(less than 0.01 percent) are separable. As the number of issues increases, the percentage of preference profiles that are separable drops. 2 To simplify the analysis, we focus on cases of two players disputing two issues, each of which has a binary outcome. In general cases of issue linkage, the two issues could be anything. In cases of economic or military sanctions, one of the issues is the source of the dispute and the other issue is whether one state imposes sanctions on the other. The two players can each have 24 possible preference rankings over combinations of outcomes, leading to 24 x 24 =576 different combinations of preference rankings between the two players. Conceivably, there are 576 variations of a two-player issuelinkage game induced by allowing only the preferences of the actors in the dispute to vary. Thus far, the theoretical literature on issue linkage (Morgan 1990, 1994) has focused only on the cases where both sides in a dispute have separable preferences. In other words, the current literature is restricted to only 8 x 8 = 64 of the possible 576 combinations of preferences for two players in a two-issue dispute. We seek to expand the literature on issue linkage to combinations of preferences in a two-player game. We also introduce incomplete information since we believe that players often do not know the true preferences of their opponents. To examine a twoperson game in which each player could have one of 576 different types of preferences would prove daunting. Luckily, analyzing all 576 different types of preferences is unnecessary since a few combinations of preferences define most cases of issue linkage involving economic or military sanctions. 2 Lacy (1997) and Lacy and Niou (1995) further divide nonseparable preferences into partially nonseparable and completely nonseparable preferences, a distinction that we do not pursue here. 8

Types of Issue Linkage In the conventional story of issue linkage (Morgan 1990), two states bargain over two issues for which their preferences are separable. The fact that the issues are separable means that each state can make concessions on the issue it cares about least without affecting its preference for the outcome of the other issue. For example, if State A s preference ranking for two issues is 10 > 11 > 00 > 01 while State B s preference ranking is 01 > 11 > 00 > 10, and if the status quo is 00, then the states can agree on 11 as a Pareto improving outcome. We define an issue linkage situation in which both states have separable preferences as Type I issue linkage. The key to Type I issue linkage is the outcome of one issue in the dispute has no impact on either state s preference for the outcome of the other issue in the dispute. Issues that become linked in international negotiations often involve nonseparable preferences on the part of one or more actors. Nonseparable preferences change the logic of issue linkage. To determine a state s preference on an issue, one must consider the outcome of the other issues in the dispute. Suppose that one of the nations, A, in a dispute over two issues has nonseparable preferences and that the other nation, B, has separable preferences. Nation A ranks the possible outcomes of the dispute as 10 > 01 > 00 > 11. Nation B, with separable preferences, ranks the outcomes 01 > 11 > 00 > 10. Both nations reveal their most preferred outcome at the beginning of a negotiation, and it is clear that they disagree since Nation A wants 10 while Nation B want 01. Nation B, following the conventional logic of issue linkage, offers 11 as an outcome, conceding on the issue that it cares least about. This offer will actually cause a setback in the negotiations since it is Nation A s least preferred outcome. Outcome 00 is agreed on by 9

both nations as the third best outcome. Both nations could do better than 00 by agreeing to 01. Nation B s best strategy is not to follow the conventional logic of issue linkage, which will only hinder the negotiation. Instead, Nation B should offer 01, which is Nation A s second best outcome. Sometimes nonseparable preferences may facilitate a resolution to a conflict. Suppose Nation A ranks outcomes 10 > 00 > 01 > 11 while Nation B ranks the outcomes 11 > 00 > 01 > 10. Both nations have nonseparable preferences. It would appear that this is a situation of complete conflict since one nation s first choice is the other nation s last. But outcome 00 is ranked second by both nations, suggesting an obvious compromise. This compromise would not be reached if the issues are treated separately since both nations first preference contains outcome 1 on issue 1. When the two sides sit at the bargaining table, they may choose to separate the issues and reach a quick agreement that 1 should be the outcome of issue 1. But then the nations enter a conflict since Nation A wants 0 on issue 2 while Nation B wants 1 on issue 2. Whichever outcome the nations choose on issue 2, the final outcome will be the worst possible to both parties. A successful negotiation would require linking these issues so that 00 is the final outcome. We call cases where one or more states has nonseparable preferences Type II issue linkage. The outcome of issue linkage is more difficult to predict under Type II linkage since the preferences of one or more states on one issue depends on the outcome of other issues. 10

An Application to Economic Sanctions and Military Coercion A large literature in international relations examines the use and success of economic sanctions (Baldwin, 1985; Galtung, 1967; Hufbauer et al., 1990; Martin, 1992; Pape, 1997; Knorr, 1975; Roger, 1996). This literature has developed separately from the literature on issue linkage, and the two literatures often do not overlap. However, economic sanctions almost by definition involve a case of issue linkage. As Martin observes, Economic sanctions are a common example of issue linkage in international politics, as states attempt to use economic levers to achieve political gains (1992, xi). We believe the same statement applies to threats of military sanctions, where a state threatens the use of military force to achieve political gains. In general, cases of sanctions (both economic and military) involve a Coercer who wants a Target to comply with the Coercer s wishes on some issue. To extract concessions on the disputed issue, X, the Coercer threatens economic or military sanctions (S) against the target. For simplicity, we assume that each issue has a binary outcome. The exhaustive set of outcomes on the issue under dispute is {Target complies, Target does not comply} = {X, ~X}. For example, if the issue is improvement of human rights in China, the set of possible outcomes is {China improves human rights, China does not improve human rights} = {X,~X}. Sanctions also involve a binary outcome, thus the set of possible outcomes is {sanctions imposed, sanctions not imposed} = {S, ~S}. We will use the convention that X = Coercer s demand met, ~X = Coercer s demand not met, S = sanctions imposed, ~S = sanctions not imposed. Now we must specify preference rankings for the Coercer and the Target in a general dispute. For the Target, we assume (~X, ~S) is the best outcome and (X,S) is the 11

worst outcome. (~X, S) and (X, ~S) are worse than (~X, ~S) but better for the Coercer than (X, S). We specify two types of targets: Resilient Targets (TR) and Compliant Targets (TC). Resilient Targets would prefer to suffer sanctions without complying with the Coercer s demands. For TR, (~X, ~S) > (~X, S) > (X, ~S) > (X,S). Note that this preference ranking is separable and lexicographic. A compliant target would rather concede on issue X than suffer economic sanctions. For TC, (~X, ~S) > (X, ~S) > (~X,S) > (X,S). This preference ranking is also separable. The Coercer may or may not have separable preferences, however. We assume that Coercers prefer not to impose economic sanctions if the target state complies on issue X, thus Coercers always prefer to avoid the costs of economic sanctions or military intervention. The Coercer might have a preference ordering (X, ~S) > (X, S) > (~X, ~S) > (~X, S). In this case, the Coercer s preferences are separable since it prefers not to impose economic sanctions regardless of its preference on X. And the Coercer prefers X > ~X regardless of its preference for sanctions. The Coercer might have a nonseparable preference ranking, such as (X, ~S) > (X, S) > (~X, S) > (~X, ~S). Given an outcome of X, the Coercer prefers ~S over S. Given an outcome of ~X, however, the Coercer prefers S over ~S. Therefore, the coercer s preference on S cannot be separated from the outcome on issue X. Such a preference ranking might be held by a state that does not want to lose credibility in international bargaining by allowing the target to continue defying the Coercer s demand while not suffering sanctions. In the game we develop, neither state knows the other state s preference ranking, thus the game is one of incomplete information. Specifically, the Target does not know 12

whether the Coercer s preferences for X and S are separable. The Coercer does not know whether the Target is resilient or compliant. Several cases of economic sanctions fall immediately under the model. In the early days of the Clinton administration, U.S. policymakers apparently wanted to grant China MFN status in exchange for improvements in China s human rights record. But without an improvement in China s human rights status, the U.S. preferred not to grant MFN status. The Clinton administration acted as though its preferences between China s trade status and the Chinese human rights record were nonseparable. The administration was likely bluffing that its preferences were nonseparable in order to induce China to improve its human rights record. The P.R.C. s government faced a strategic decision characterized by incomplete information about the Clinton administration s preferences. We can model this strategic interaction as a game between the P.R.C. and a U.S. administration that could have either separable or nonseparable preferences for trade and human rights improvements. The outcome of the dispute will depend critically on whether the U.S. actually has separable preferences and whether the P.R.C. believes that the U.S. has separable preferences. An actor in a dispute, in this case the Clinton administration, may find strategic opportunities in a negotiation by claiming to have nonseparable preferences across several issues even if the actor s true preferences are separable. In the case of China s most favored nation status, the P.R.C. called the U.S. bluff, and the Clinton administration proved willing to accept China as a most favored trading partner without improvements in China s human rights record. 13

As a second example of the sanctions game, consider the UN position against Iraq. The UN, to the extent it can be called a unitary actor, prefers that Iraq scrap its biological and chemical weapons program, or else the UN nations will impose economic and military sanctions against Iraq. The UN s preferences appear nonseparable. Iraq may at times believe that the UN s preferences are actually separable, such that the UN prefers not to impose sanctions on Iraq regardless of the status of Iraq s weapons program. Our model of economic sanctions is a game with two players: the Coercer and the Target. The game begins with the Coercer first choosing between linking and not linking sanctions to some other issue, X, followed by the target s decision between capitulating to the threat or ignoring the threat. If the Target ignores the threat of sanctions, the Coercer must decide whether to escalate the conflict or delink the two issues. To capture uncertainty in the players interactions and to determine how the structure affects optimal strategies, we assume that Target assesses probability p that the Coercer has nonseparable preferences and probability 1-p that the Target has separable preferences. The Coercer assesses with probability q that the Target is resilient and probability 1-q that it is compliant. There are four possible outcomes: Status Quo: (~S, X): the Coercer decides not to link sanctions to issue X the Coercer decides to link the two issues together and the Target capitulates (S, X): the Coercer decides to link the two issues, the Target resists, and the Coercer imposes sanctions 14

(~S, X): the Coercer decides to link the two issues, the Target resists, and the Coercer decides to delink the two issues. We omit (S,X) as an outcome since we assume that the Coercer will not impose sanctions once the Target capitulates to its demands on issue X. The status quo (SQ) implies an outcome (~S,~X), but the players receive different payoffs from the status quo than they do from the adoption of strategies that lead to (~S,~X). The Target prefers (~S, X) to SQ because the decision for the Coercer to delink helps Target to update its belief about the Coercer type and to gain credibility as resilient. The Target s decision to ignore the threat also influences the Coercer s belief about Target s type. The Coercer prefers SQ over (~S,~X) due to the loss of credibility that comes from backing down after threatening to link issues or impose sanctions. From Target's perspective, (~S, X) and SQ are the best and second best outcomes regardless of its type. Regarding the other two outcomes, a Resilient Target would prefer (S, X) to (~S,X), whereas a Compliant Target would have the reverse preference ordering. The preference orderings can be assigned in a similar fashion for the Coercer. The Coercer always most prefers (~S, X) regardless of its type. If the Coercer has nonseparable preferences, it prefers (S, X) to SQ to (~S, X), whereas a Coercer with separable preferences would prefer SQ to (~S, X) to (S, X). Table 1 summarizes the outcomes and payoffs for the two players, with payoffs specified as ordinal utilities from most preferred (1) to least preferred (4). 15

Table 1 Payoffs for Target (Separable or Nonseparable) and Coercer (Resilient or Compliant) Target Coercer Outcome Resilient Compliant Nonsep. Separable SQ w2 x2 y3 z2 (~S, X) w4 x3 y1 z1 (S, X) w3 x4 y2 z4 (~S, X) w1 x1 y4 z3 Figure 1 portrays the extensive form game of this two-player game with two-sided incomplete information. Given the preference rankings and looking backwards along the game tree, if Target does not capitulate on the disputed issue, the Coercer will escalate the conflict if it has nonseparable preferences and will delink if it has separable preferences. If the Target is resilient, its dominant strategy is not to give in on the disputed issue. Further, we can see that if the Coercer has nonseparable preferences, then it is always in its interest to link the two issues; that is, it will always choose sanctions over backing down. We can now solve the game by constructing its normal form using the following strategies for Target and Coercer. For the Coercer, we have shown that if the Coercer has nonseparable preferences, it will always choose to link the issues. If the Coercer has separable preferences, however, its strategies are to link or not to link trade Target s compliance on issue X. Thus: L L: link if the Coercer has nonseparable preferences, do not link if separable; LL: link regardless of its type. For Target, the strategies are: R R: resist if Target is resilient, capitulate if compliant; 16

RR: resist regardless of its type. Table 2 represents the normal form of the extensive form game illustrated in Figure 1. To see how we can now determine the payoffs in one cell of the game's normal form, suppose that the Coercer chooses LL and Target chooses R R. Given this strategy pair, one of the following four outcomes can occur. First, the Coercer has nonseparable preferences (with probability p) and Target is resilient (with probability q); the outcome is y2 for the Coercer and w3 for Target. Second, the Coercer has nonseparable preferences (with probability p) and Target is compliant (with probability 1-q); the outcome is y1 for the Coercer and x3 for the Coercer. Third, the Coercer has separable preferences (with probability 1-p) and Target is resilient (with probability q); the outcome is z3 for the Coercer and w1 for Target. Fourth, the Coercer has separable preferences (with probability 1-p) and Target is resilient (with probability 1-q); the outcome is z1 for the Coercer and x3 for Target. Thus, with (LL, R R), the expected payoff for the Coercer is pqy2 + p(1-q)y1 + (1-p)qz3 + (1-p)(1-q)z1, and for Target it is pqw3 + p(1-q)x3 + (1-p)qw1 + (1-p)(1-q)x3. Table 2 portrays this situation's full normal form. Table 2: Normal Form Representation of the Coercer-Target Game Coercer LL L L Target RR R R pqy2+p(1-q)y2+(1-p)qz3+(1-p)(1-q)z3 pqy2+p(1-q)y1+(1-p)qz3+(1-p)(1-q)z1 pqw3+p(1-q)x4+(1-p)qw1+(1-p)(1-q)x1 pqw3+p(1-q)x3+(1-p)qw1+(1-p)(1-q)x3 pqy2+p(1-q)y2+(1-p)qz2+(1-p)(1-q)z2 pqy2+p(1-q)y1+(1-p)qz2+(1-p)(1-q)z2 pqw3+p(1-q)x4+(1-p)qw2+(1-p)(1-q)x2 pqw3+p(1-q)x3+(1-p)qw2+(1-p)(1-q)x2 17

Two strategy-pairs, (LL, R R) and (L L, R R) could satisfy the definition of equilibria. We first examine the strategy-pair, (LL, R R). For this strategy pair to be an equilibrium, neither Coercer nor Target would have incentives to deviate from the prescribed strategies. This implies that for (LL, R R) to be an equilibrium, the following inequalities must be satisfied. qz3 + (1-q)z1 > z2 (1) (1-p)x1 + px4 < x3 (2) Now considering inequality (1), ceteris paribus, for the Coercer with separable preferences, if Target is likely to be compliant (q is low), if the cost of delinking is relatively small or if the value of issue X is relatively larger than the status quo (z2-z3 is low or z1-z2 is high), it is more likely that the Coercer will bluff. Therefore, Coercers with separable preferences will behave as though their preferences are nonseparable. For the Compliant Target, inequality (2) suggests that Target will not deviate from the current strategy if the Coercer is likely to have nonseparable preferences (p is large), if the cost of complying on issue X is relatively low (x1-x3 is low), or if the cost of sanctions is relatively high (x3-x4 is high). When inequality (1) is not satisfied, (L L, R R) becomes the equilibrium. That is, if Target is likely to be resilient (q is high), if the cost of delinking is relatively high or if the value of X is relatively lower than the status quo (z2-z3 is high or z1-z2 is low), it is more likely that the Coercer will choose not to link the two issues in the first place when it has separable preferences. Several features of this example underscore the more general model, which has yet to be specified in the literature on issue linkage. First, the game involves incomplete 18

information on the parts of both players. The Target does not know the preferences of the Coercer. Specifically, it does not know if the Coercer has separable or nonseparable preferences for sanctions and issue X. States may have incentives to bluff about their preferences in order to gain a bargaining advantage. The Coercer would like the Target to think that the Coercer s preferences are nonseparable. In the case of US-China bargaining over human rights and MFN status, the Clinton administration initially wanted to appear as though it had nonseparable preferences even though, in the end, it appears that the Clinton administration had separable preferences for trade and human rights improvements in China. Second, the beliefs of each player about the other player s type enter into the game. Uncertainty is a key ingredient of the model, which distinguishes our work from much of the existing literature on issue linkage. If players were certain about each other s type, then linkage would not be necessary or desirable unless there were clear Pareto improvements to be gained from linkage. Issue linkages such as economic sanctions, especially when unsuccessful, indicates incomplete information on the part of one or more players. The specific form of the game the players, their payoffs, and their strategies may vary from situation to situation. But the general framework of the game will not. In cases of issue linkage in international politics, two or more players having either separable or nonseparable preferences enter a game of incomplete information. Discussion We develop in this paper a framework for the study of issue linkage, including special cases such as economic sanctions and military coercion. By expanding 19

conventional models of issue linkage to include nonseparable preferences, we are able to examine a wider variety of linkage situations than past models have examined. While we examine only a few of the possible combinations of preferences in a two-player issue linkage game, our game-theoretic framework can be adapted easily to other combinations of players preferences. The model in this paper represents many cases of economic or military sanctions. Typologies of issue linkage based on the nature of the issues or the success of the linkage miss the most important variable in the game: the preferences of the players. Long-standing models of issue linkage and economic sanctions assume that all players have separable preferences for the issues involved. When players have nonseparable preferences, then the logic of issue linkage changes. Nonseparable preferences may provide one answer to the empirical puzzle of how issue linkage has proven so unsuccessful as a means to resolve international conflicts. 20

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Table 1: Types of Preferences Over Binary Outcomes on 2 Issues Preference Ordering Type 00 > 01 > 10 > 11 Separable 00 > 01 > 11 > 10 Nonseparable 00 > 10 > 01 > 11 Separable 00 > 10 > 11 > 01 Nonseparable 00 > 11 > 01 > 10 Nonseparable 00 > 11 > 10 > 01 Nonseparable 01 > 00 > 10 > 11 Nonseparable 01 > 00 > 11 > 10 Separable 01 > 10 > 00 > 11 Nonseparable 01 > 10 > 11 > 00 Nonseparable 01 > 11 > 00 > 10 Separable 01 > 11 > 01 > 00 Nonseparable 10 > 00 > 01 > 11 Nonseparable 10 > 00 > 11 > 01 Separable 10 > 01 > 00 > 11 Nonseparable 10 > 01 > 11 > 00 Nonseparable 10 > 11 > 00 > 01 Separable 10 > 11 > 01 > 00 Nonseparable 11 > 00 > 01 > 10 Nonseparable 11 > 00 > 10 > 01 Nonseparable 11 > 01 > 00 > 10 Nonseparable 11 > 01 > 10 > 00 Separable 11 > 10 > 00 > 01 Nonseparable 11 > 10 > 01 > 00 Separable 23

link capitulate escalate w4, y1 w3, y2 ignore Resilient q 1-q Compliant Nonseparable p 1-p Resilient Separable q 1-q Target delink w2, y3 no link Coercer capitulate Coercer link escalate ignore delink x2, y3 no link capitulate link escalate ignore Target delink w2, z2 no link Coercer Coercer capitulate link escalate w1, y4 x3, y1 x4, y2 x1, y4 w4, z1 w3, z4 w1, z3 x3, z1 x4, z4 Compliant ignore delink x1, z3 no link x2, z2