George Mason University SCHOOL of law THE ROLE OF RECIPROCITY IN INTERNATIONAL LAW 02-08 francesco Parisi and nita ghei LAW AND ECONOMICS WORKING PAPER SERIES This paper can be downloaded without charge from the Social Science Research Network Electronic Paper Collection http://ssrn.com/abstractid=307141
George Mason University SCHOOL of LAW INTERNATIONAL LAW 02-08 Francesco Parisi and Nita Ghei LAW AND ECONOMICS WORKING PAPER SERIES This paper can be downloaded without charge from the Social Science Research Network Electronic Paper Collection: http://ssrn.com/abstract_id=307141 THE ROLE OF RECIPROCITY IN
THE ROLE OF RECIPROCITY IN INTERNATIONAL LAW Francesco Parisi and Nita ghei INTRODUCTION contented with so much liberty against other men as he would allow other men against himsel/'6 [A] man be willing, when others are too, as far forth for peace and defense of himself, The concept of reciprocity assumes peculiar importance in a world where there is no external authority to enforce agreements, that is, in a world that exists in Hobbesian state of nature Historically, norms of reciprocity have been vital is escaping lives that would otherwise be"solitary poor, nasty, brutish and short. Reciprocity generally involves returning like behavior with like In Robert Axelrod's terminology, reciprocity is a tit-for-tat strategy. Such a strategy permits cooperation in a state of nature, when no authority for enforcement of agreements exists International law, in this sense, exists in a state of nature- there is no overarching legal authority with compulsory jurisdiction to enforce agreements. Inevitably, reciprocity has become an important element in the practice of sovereign nations and in the body of existing international law This paper begins with setting up a taxonomy of social interactions in a game-theoretic framework,t Professor of Law and Director, International Business Law Program, George Mason University School of Law, Co-Director, James M. Buchanan Program in Economics and the Law Robert A. Levy Fellow in Law and Liberty. George Mason University School of Law. J D. candidate lay 2002, George Mason University School of Law, Ph. D, 1992, Department of Economics, University of Maryland, College Park; B.A. (Honors)in Economics, 1985, Delhi University, India The second law of nature, according to Hobbes. THOMAS HOBBES, LEVIATHAN, (1651)(Liberal Arts Press 1958)at 110 See hobbes supra note I at 107 See generally ROBERT AXELROD, THE EVOLUTION OF COOPERATION (1984). Axelrod demonstrates the superiority of a cooperative strategy when people undertake repeated interactions over a strategy that would seemingly be rational in a Prisoner's Dilemma situation, discussed infra Part I.C. An earlier, somewhat different, version of this taxonomy is found in Francesco Parisi, The Cost of the ame: A Taxonomy of Social Interactions, 9 Eur J. L. Econ. 99(2000)(hereinafter Parisi, Taxonomy)
* Professor of Law and Director, International Business Law Program, George Mason University School of Law; Co-Director, James M. Buchanan Program in Economics and the Law. **Robert A. Levy Fellow in Law and Liberty. George Mason University School of Law. J.D. candidate, May 2002, George Mason University School of Law; Ph.D., 1992, Department of Economics, University of Maryland, College Park; B.A. (Honors) in Economics, 1985, Delhi University, India. 1 The second law of nature, according to Hobbes. THOMAS HOBBES, LEVIATHAN, (1651) (Liberal Arts Press 1958) at 110. 2 See Hobbes supra note 1 at 107. 3 See generally ROBERT AXELROD, THE EVOLUTION OF COOPERATION (1984). Axelrod demonstrates the superiority of a cooperative strategy when people undertake repeated interactions over a strategy that would seemingly be rational in a Prisoner’s Dilemma situation, discussed infra Part I.C. 4An earlier, somewhat different, version of this taxonomy is found in Francesco Parisi, The Cost of the Game: A Taxonomy of Social Interactions, 9 Eur. J. L. Econ. 99 (2000) (hereinafter Parisi, Taxonomy). 1 THE ROLE OF RECIPROCITY IN INTERNATIONAL LAW Francesco Parisi* and Nita Ghei** INTRODUCTION [A] man be willing, when others are too, as far forth for peace and defense of himself, . .. , be contented with so much liberty against other men as he would allow other men against himself.1 The concept of reciprocity assumes peculiarimportance in a world where there is no external authority to enforce agreements, that is, in a world that exists in Hobbesian state of nature. Historically, norms of reciprocity have been vital is escaping livesthat would otherwise be “solitary, poor, nasty, brutish and short.”2 Reciprocity generally involves returning like behavior with like. In Robert Axelrod’s terminology, reciprocity is a tit-for-tat strategy.3 Such a strategy permits cooperation in a state of nature, when no authority for enforcement of agreements exists. International law, in this sense, exists in a state of nature - there is no overarching legal authority with compulsory jurisdiction to enforce agreements. Inevitably, reciprocity has become an important element in the practice of sovereign nations and in the body of existing international law. This paper begins with setting up a taxonomy ofsocial interactionsin a game-theoretic framework,4
to examine the role of reciprocity in the functioning of international law and whether reciprocity is in effect. a meta-rule for the law of nations Part I defines the characteristics of specific types of interactions between countries in a game theoretic framework. Part II sets out definitions for different forms of reciprocity found in international law. We then examine the international law settings where reciprocity constraints would yield an optimal outcome, and when such constraints would be ineffective. Part Ill sets out specific examples from international law, and see where they fit in the taxonomy of the games formulated. This makes clear that the principle of reciprocity is of vital importance in achieving efficient outcomes in many circumstances. Finally, in Part Iv, we conclude that despite the occasional failure, reciprocity is important enough to be considered a meta-rule of the system of international law- an essential element in its functioning . RECIPROCITY THROUGH THE LENS OF GAME THEORY. A TAXONOMY Game theory is a useful tool for the study of international law and the relations between sovereign states, since it focuses on interactions where parties can determine only their own strategies and thus have no direct control of the outcome. The outcome results from the joint interaction of the strategies chosen by independent players. That is, parties can choose their strategies but cannot directly determine the outcome by their own actions. For the purpose of our analysis, we distinguish five broad categories of relevant interactions, which provide a useful taxonomy for the fina/ou The general world of game theory is one where a player can control only their own strategies, but not the ome. See, e.g, THOMAS SCHELLING, THE STRATEGY OF CONFLICT(1980 ed)(discussing issues of war and strategy ) For a very brief and basic introduction to game theory, see ROBERT COOTER aND THOMAS ULEN, LAW AND ECONOMICS(3 ded. 2000)at 34-39
5 The general world of game theory is one where a player can control only their own strategies, but not the final outcome. See, e.g., THOMAS SCHELLING, THE STRATEGY OF CONFLICT (1980 ed) (discussing issues of war and strategy). For a very brief and basic introduction to game theory, see ROBERT COOTER aND THOMAs ULEN, LAW AND ECONOMICS (3rd ed. 2000) at 34-39. 2 to examine the role of reciprocity in the functioning of international law and whether reciprocity is, in effect, a meta-rule for the law of nations. PartI definesthe characteristics ofspecific types ofinteractions between countriesin a gametheoretic framework. Part II sets out definitions for different forms of reciprocity found in international law. We then examine the international law settings where reciprocity constraints would yield an optimal outcome, and when such constraints would be ineffective. Part III sets out specific examples from international law, and see where they fit in the taxonomy of the games formulated. This makes clear that the principle of reciprocity is of vital importance in achieving efficient outcomes in many circumstances. Finally, in Part IV, we conclude that despite the occasional failure, reciprocity is important enough to be considered a meta-rule of the system of international law - an essential element in its functioning. I. RECIPROCITY THROUGH THE LENS OF GAME THEORY: A TAXONOMY Game theory is a useful tool for the study of international law and the relations between sovereign states, since it focuses on interactions where parties can determine only their own strategies and thus have no direct control of the outcome.5 The outcome results from the joint interaction ofthe strategies chosen by independent players. That is, parties can choose their strategies but cannot directly determine the outcome by their own actions. For the purpose of our analysis, we distinguish five broad categories of relevant interactions, which provide a useful taxonomy for the
understanding of international relations. In each case, the payoff for Player A is represented by the first number in a cell; the payoff for Player B is represented by the second figure. Each player has three possible payoffs. Generally, the greater the level of cooperation, the greater the combined pay off Strategy I represents full cooperation; strategy II represents partial cooperation; and strategy Ill represents a situation where neither party chooses to cooperate Imposing a reciprocity constraint means that the choice of strategy is determined mutually hus, if Player A chooses to cooperate, under a reciprocity constraint, Player B will have to cooperate, If Player A chooses Strategy Ill, and not cooperate, Player B will also choose Strategy Ill Both parties know that the imposition of a reciprocity constraint limits interaction, so that options on the diagonal. as shown in Figure 2. are left available A. Pure Common-Interest Situations In game theory, this group of situations are represented as positive sum games with a single dominant strategy that leads to efficient outcomes. This optimal outcome is achievable by the parties in a stable Nash equilibrium. This category has been categorized by Thomas Schelling as a pure common interest game. As the optimal outcome is a Nash equilibrium, where the party's incentives are perfectly aligned, any implicit or explicit agreement between the parties becomes self-enforcing, in the sense that no party has an interest to deviate unilaterally. a sample pay-off matrix in such a game could take the following form: This draws heavily on Parisi, Taxonomy, supra note 4 A Nash equilibrium is a situation where no individual player can do better by changing strategy, as long as the other party does not change strategy. Thus, neither party has any incentive to change the choice made. See Cooter and Ulen, supra note 5 at 37. See Schelling supra note 5 at 88
6 This draws heavily on Parisi, Taxonomy, supra note 4. 7A Nash equilibrium is a situation where no individual player can do better by changing strategy, as long as the other party does not change strategy. Thus, neither party has any incentive to change the choice made. See Cooter and Ulen, supra note 5 at 37. 8 See Schelling supra note 5 at 88. 3 understanding of international relations.6 In each case, the payoff for Player A is represented by the first number in a cell; the payoff for Player B is represented by the second figure. Each player has three possible payoffs. Generally, the greater the level of cooperation, the greater the combined payoff. Strategy I represents full cooperation; strategy II represents partial cooperation; and strategy III represents a situation where neither party chooses to cooperate. Imposing a reciprocity constraint means that the choice of strategy is determined mutually. Thus, if Player A chooses to cooperate, under a reciprocity constraint, Player B will have to cooperate, If Player A chooses Strategy III, and not cooperate, Player B will also choose Strategy III. Both parties know that the imposition of a reciprocity constraint limits interaction, so that options on the diagonal, as shown in Figure 2, are left available. A. Pure Common-Interest Situations In game theory, this group of situations are represented as positive sum games with a single dominantstrategy that leadsto efficient outcomes. This optimal outcome is achievable by the parties in a stable Nash equilibrium.7 This category has been categorized by Thomas Schelling as a pure common interest game.8 As the optimal outcome is a Nash equilibrium, where the party’s incentives are perfectly aligned, any implicit or explicit agreement between the parties becomesself-enforcing, in the sense that no party has an interest to deviate unilaterally. A sample pay-off matrix in such a game could take the following form:
II III I4,22,10.0 Figure(1): A Pure Common Interest Game Both parties, following individually rational strategies which maximize payoffs would choose to follow Strategy I, for a payoff of 6 units each. The outcome remains unchanged if a reciprocity constraint is imposed
4 Figure (1): A Pure Common Interest Game Both parties, following individually rational strategies which maximize payoffs would choose to follow Strategy I, for a payoff of 6 units each. The outcome remains unchanged if a reciprocity constraint is imposed:
II 6,6-4,5|2,4 II|5,43,31,2 I4,22,10,0 Figure(2): A Pure Common interest Game with Reciprocity The cooperation outcome, with a payoff of 6 units for each player, remains the dominant strategy even with the imposition of a reciprocity constraint, and there is no incentive for either party to deviate from this outcome This amounts to the notion termed, in the economics literature,"perfect incentive alignment. This game's payoff structure excludes the possibility of opportunistic behavior. One could think of this ideal environment as the result of optimal contract enforcement mechanisms, institutional safeguards, relationships involving trust and reputation, or any other device which renders adversarial possibilities non advantageous or inaccessible to the players Generally speaking, solutions to this class of games are not troublesome, since all players gain by cooperating. Perfect incentive alignment guarantees that the spontaneous equilibrium of the sEe Parisi, Taxomony, supra note 4 and Schelling, supra note I See generally, Cooter and Ulen, supra note 5 for a discussion of the interaction of game theory and the law. They use game theory as an analytical toot to discuss contract law. ld. at 184-198
9 See Parisi, Taxomony, supra note 4 and Schelling, supra note 5. 10See generally, Cooter and Ulen, supra note 5 for a discussion of the interaction of game theory and the law. They use game theory as an analytical toot to discuss contract law. Id. at 184-198. 5 Figure (2): A Pure Common Interest Game with Reciprocity The cooperation outcome, with a payoff of 6 units for each player, remains the dominant strategy even with the imposition of a reciprocity constraint, and there is no incentive for either party to deviate from this outcome. This amounts to the notion termed, in the economics literature, “perfect incentive alignment.”9 This game’s payoff structure excludes the possibility of opportunistic behavior. One could think of this ideal environment as the result of optimal contract enforcement mechanisms, institutional safeguards, relationships involving trust and reputation, or any other device which renders adversarial possibilities non advantageous or inaccessible to the players.10 Generally speaking, solutions to this class of games are not troublesome, since all players gain by cooperating. Perfect incentive alignment guaranteesthat the spontaneous equilibrium of the
game will occur at an optimizing point Whether the incentive-alignment is endogenous or exogenously determined by existing laws or norms, there is no need for additional intervention in either situation Real life situations of common interest games are common, but hard to illustrate with international law examples, because, unlike other strategic situations, common interest situations are self-enforcing and rarely emerge to engage the attention of international actors and policymakers as levant international legal issues. As long as interests of all parties converge, no dispute will arise that needs resolution by resort to a treaty or other legal instruments Nonetheless, situations do develop that ultimately reflect features of a common interest game. An example of this is the custom in international law regarding the Continental Shelf that developed following the Truman Proclamation of 1945. This is discussed in greater detail below, however the punch line is that it was in the interest of all coastal states to cooperate with the United States on the matter, even though the proclamation was inconsistent with existing international law I Similarly, pure coordination problems are characterized by the perfect convergence of the players' interests and by the additional feature of multiple equilibria. The convergence of individual and collective inter fosters an optimal outcome on the basis of a mere coordination of self-interested strategies. It has been arguecests processes of legal and social order. The multiplicity of Nash equilibria in a coordination game creates difficulties for decentralized solutions. For example, if everyone in a country needs to coordinate on a basic set of traffic conventions, such as driving on the same side of the road, the emergence of spontaneous )but heterogeneous in a modern society. Ironically, however, the most universal traffic rules are those for water navigation, which Quired clusters of traffic customs would consolidate local equilibria that do not possess the features of universality red emerged through spontaneous rule-making processes. For an interesting historical background, see JOHN H WIGMORE, THE MARITIME LEGAL SYSTEM, (1928), see generally, NICHOLAS J. HEALY DAVID J. SHARPE, ADMIRALTY CASES AND MATERIALS, (2nd ed, 1986): IAN BROWNLIE, PRINCIPLES OF PUBLIC INTERNATIONAL LAW (4th ed, 1990); THOMAS J SCHOENBAUM, ADMIRALTY AND MARITIME LAW, (1987). The issue of reciprocity in the Law of the Sea is discussed further infra Part IIIC See discussion infra Part Ill.A. The discussion is based largely on Brownlie, supra note 11, and MICHAEL BYERS, CUSTOM, POWER AND THE POWER OF RULES (1999). The incentive alignment is among the coastal states; in effect, non-coastal states are treated as non-participants 6
11 Similarly, pure coordination problems are characterized by the perfect convergence of the players’ interests and by the additional feature of multiple equilibria. The convergence of individual and collective interests fosters an optimal outcome on the basis of a mere coordination of self-interested strategies. It has been argued, however, that the solution to coordination problems may be delayed if it relies exclusively on decentralized processes of legal and social order. The multiplicity of Nash equilibria in a coordination game creates difficulties for decentralized solutions. For example, if everyone in a country needs to coordinate on a basic set of traffic conventions, such as driving on the same side of the road, the emergence of spontaneous ) but heterogeneous ) clusters of traffic customs would consolidate local equilibria that do not possess the features of universality required in a modern society. Ironically, however, the most universal traffic rules are those for water navigation, which emerged through spontaneous rule-making processes. For an interesting historical background, see JOHN H. WIGMORE, THE MARITIME LEGAL SYSTEM, (1928); see generally, NICHOLAS J. HEALY & DAVID J. SHARPE, ADMIRALTY CASES AND MATERIALS, (2nd ed., 1986); IAN BROWNLIE, PRINCIPLES OF PUBLIC INTERNATIONAL LAW (4th ed., 1990); THOMAS J. SCHOENBAUM, ADMIRALTY AND MARITIME LAW, (1987). The issue of reciprocity in the Law of the Sea is discussed further infra Part III.C. 12See discussion infra Part III.A. The discussion is based largely on Brownlie, supra note 11, and MICHAEL BYERS, CUSTOM, POWER AND THE POWER OF RULES (1999). The incentive alignment is among the coastal states; in effect, non-coastal states are treated as non-participants. 6 game will occur at an optimizing point.11 Whether the incentive-alignment is endogenous or exogenously determined by existing laws or norms, there is no need for additional intervention in either situation. Real life situations of common interest games are common, but hard to illustrate with international law examples, because, unlike other strategic situations, common interest situations are self-enforcing and rarely emerge to engage the attention of international actors and policymakers as relevant international legal issues. As long as interests of all parties converge, no dispute will arise that needs resolution by resort to a treaty or other legal instruments. Nonetheless, situations do develop that ultimately reflect features of a common interest game. An example of thisisthe custom in international law regarding the Continental Shelf that developed following the Truman Proclamation of 1945.12 This is discussed in greater detail below; however the punch line is that it wasin the interest of all coastalstatesto cooperate with the United States on the matter, even though the Proclamation was inconsistent with existing international law
B Divergent Preference Games This class of games encompasses positive sum games with multiple Nash equilibria, where the different equilibria are the result of differences in preferences, and not strategic behavior. These games are characterized by mixed conflict-coordination motives. In the literature, these games are often called Battle of the Sexes games. 3 Coordination problems in such games could be solved by permitting sequential decision-making or pre-commitment strategies. In situations where the players engage in games repeatedly, a norm of fairness may be sufficient to address the problem of a sub optimal conflictual outcome, if the discount rates of the parties are sufficiently small For a one-time game, a pay-off matrix for a Divergent Preference game could look like this II 0,0|0,0 I0,02,30,0 I0,00,0 Figure(3): Divergent Preference Game In this case, there are three Nash equilibria, along the diagonal, with no single dominant outcome \See Parisi, Taxonomy, supra note 4
13See Parisi, Taxonomy, supra note 4. 7 B. Divergent Preference Games This class of games encompasses positive sum games with multiple Nash equilibria, where the different equilibria are the result of differences in preferences, and not strategic behavior. These games are characterized by mixed conflict-coordination motives. In the literature, these games are often called Battle of the Sexes games.13 Coordination problems in such games could be solved by permitting sequential decision-making or pre-commitmentstrategies.In situations where the players engage in games repeatedly, a norm of fairness may be sufficient to address the problem of a suboptimal conflictual outcome, if the discount rates of the parties are sufficiently small. For a one-time game, a pay-off matrix for a Divergent Preference game could look like this: Figure (3): Divergent Preference Game In this case, there are three Nash equilibria, along the diagonal, with no single dominant outcome
Nor do matters improve with a reciprocity constraint, if the game is played a single time. The pay- off matrix for a Divergent Preference game with a reciprocity constraint would take the following for 0,0|0,0 I|0,02 0 00.01,5 Figure( 4): Divergent Preference Game under reciprocity The [Ill, Ill] cell would yield the highest total payoff, and is the most desirable in terms of maximizing total welfare But player a prefers Strategy I and Player Ill prefers strategy Ill. Imposing a reciprocity constraint does not change this preference ordering. It might still be possible to achieve
8 Nor do matters improve with a reciprocity constraint, if the game is played a single time. The payoff matrix for a Divergent Preference game with a reciprocity constraint would take the following form: Figure (4): Divergent Preference Game under Reciprocity The [III,III] cell would yield the highest total payoff, and is the most desirable in terms of maximizing total welfare. But player A prefers Strategy I and PlayerIII prefersstrategy III.Imposing a reciprocity constraint does not change this preference ordering. It mightstill be possible to achieve
the outcome with the highest total outcome. If players are in the game repeatedly, or if there is possibility of role reversibility, the players may choose to cooperate to maximize total payoffs over all periods C. Prisoners Dilemma situations This is probably the best known and most widely used set of games. a prisoners dilemma game is game with a surplus obtainable through the parties' cooperation, but has dominant defection strategies which yield a sub-optimal outcome for both players, when both players follow a strategy that is privately rational. In such games, defection strategies are dominant, and the possibility of opportunistic behavior renders the Pareto optimal outcome unachievable in equilibrium. A pay-off matrix for a Prisoner's Dilemma game could have the following form Role reversibility, where any person could be on either side of a dispute, can lead to stable norms that yield efficient outcomes over time. This is accomplished by stochastic reciprocity, see discussion infra Part Il. The medieval law merchant provides one example. see Francesco Parisi, Customary Law in THE NEW PALGRAVE DICTIONARY OF ECONOMICS AND THE LAW (hereinafter, Parisi, Customary Law). See also, ROBERT C ELLICKSON ORDER WITHOUT LAW: HOW NEIGHBORS SETTLE DISPUTES (1991). Ellickson discusses the mechanisms of informal dispute settlement that have evolved among ranchers in Shasta County, California. In international law, role reversibility is at the heart of the reciprocity that is integral to the Law of the Sea as it has developed over time, as discussed infra Part Ill.C
14Role reversibility, where any person could be on either side of a dispute, can lead to stable norms that yield efficient outcomes over time. This is accomplished by stochastic reciprocity, see discussion infra Part II. The medieval law merchant provides one example. see Francesco Parisi, Customary Law in THE NEW PALGRAVE DICTIONARY OF ECONOMICS AND THE LAW (hereinafter, Parisi, Customary Law). See also, ROBERT C. ELLICKSON, ORDER WITHOUT LAW: HOW NEIGHBORS SETTLE DISPUTES (1991). Ellickson discusses the mechanisms of informal dispute settlement that have evolved among ranchers in Shasta County, California. In international law, role reversibility is at the heart of the reciprocity that is integral to the Law of the Sea as it has developed over time, as discussed infra Part III.C. 9 the outcome with the highest total outcome. If players are in the game repeatedly, or if there is a possibility of role reversibility, the players may choose to cooperate to maximize total payoffs over all periods.14 C. Prisoners’ Dilemma Situations This is probably the best known and most widely used set of games. A prisoners dilemma game is game with a surplus obtainable through the parties’ cooperation, but has dominant defection strategies which yield a sub-optimal outcome for both players, when both players follow a strategy that is privately rational. In such games, defection strategies are dominant, and the possibility of opportunistic behavior renders the Pareto optimal outcome unachievable in equilibrium. A pay-off matrix for a Prisoner’s Dilemma game could have the following form:
