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: