II III 0 Figure(5): A Prisoner's Dilemma Problem Figure 5 depicts the equilibrium obtained in the absence of a reciprocity constraint. Two players are faced with a cooperation problem. Strategies L, Il, and Ill represent three successively lower levels of cooperation. Even though mutual cooperation at level i generates the highest aggregate payoff, strategy Ill, no cooperation, dominates in equilibrium, as it is shown by the Nash arrows for the two players
10 Figure (5): A Prisoner’s Dilemma Problem Figure 5 depicts the equilibrium obtained in the absence of a reciprocity constraint. Two players are faced with a cooperation problem. Strategies I, II, and III represent three successively lower levels of cooperation. Even though mutual cooperation at level I generates the highest aggregate payoff, strategy III, no cooperation, dominates in equilibrium, as it is shown by the Nash arrows for the two players
In this case the cell(6, 6), which represents the mutual cooperation outcome, is the Pareto-optimal outcome, but the cell(0, 0), which represents the mutual defection outcome is the dominant trategy Parisi has pointed out that reciprocity constraints are extraordinarily well-suited for Prisoners' Dilemma situations. International law is rich in telling illustrations of the power of reciprocity constraints in correcting or preventing Prisoner's Dilemma situations. For example, a reciprocity constraint, such as that established in Article 21(b )of the Vienna Convention of 1969 eliminates the possibility of opportunistic behavior, and makes the Pareto-optimal cooperation outcome feasible D. Inessential Games There are two kinds of games in this category: (i) zero-sum games and (ii) positive sum games where all obtainable Nash equilibria have a constant aggregate payoff All these games are characterized by constant pay-offs, and no single outcome is mutually preferred by the two players Territorial disputes are an example of this set of games. As it will be discussed more extensively below, it is impossible to design a reciprocity constraint that could have any effect on the strategic behavior of the parties. Consider, for example, the territorial dispute between India and Pakistan over A Pareto optimum is achieved when it is no longer possible to make anyone better off without making at least one person worse off. See generally, E.B. MISHAN, AN INTRODUCTION TO NORMATIVE ECONOMICS See Parisi, Taxonomy, supra note 4 Vienna Convention on The Law of Treaties, opened for signature May 23, 1969, Art. 21, 1155 U.N.T.S 331(hereinafter Vienna Convention)
15A Pareto optimum is achieved when it is no longer possible to make anyone better off without making at least one person worse off. See generally, E.B.MISHAN, AN INTRODUCTION TO NORMATIVE ECONOMICS. 16See Parisi, Taxonomy, supra note 4. 17Vienna Convention on The Law of Treaties, opened for signature May 23,1969, Art. 21, 1155 U.N.T.S. 331 (hereinafter Vienna Convention). 11 In this case the cell (6,6), which represents the mutual cooperation outcome, is the Pareto-optimal outcome,15 but the cell (0,0), which represents the mutual defection outcome is the dominant strategy. Parisi has pointed out that reciprocity constraints are extraordinarily well-suited for Prisoners’ Dilemma situations.16 International law is rich in telling illustrations of the power of reciprocity constraints in correcting or preventing Prisoner’s Dilemma situations. For example, a reciprocity constraint, such as that established in Article 21(b) of the Vienna Convention of 196917 , eliminates the possibility of opportunistic behavior, and makes the Pareto-optimal cooperation outcome feasible. D. Inessential Games There are two kinds of games in this category: (i) zero-sum games and (ii) positive sum games where all obtainable Nash equilibria have a constant aggregate payoff All these games are characterized by constant pay-offs, and no single outcome is mutually preferred by the two players. Territorial disputes are an example of this set of games. As it will be discussed more extensively below, it is impossible to design a reciprocity constraint that could have any effect on the strategic behavior ofthe parties.Consider,for example, the territorial dispute between India and Pakistan over
Kashmir. This is the quintessential zero-sum game- the territory can go to only one country. The gain to one country is exactly equal to the loss to the other, since the territory is available in a fixed amount. There is no way the winner can compensate the loser; there is no potential gain from Itual cooperation and, consequently, here is no role for reciprocity constraints in such a situatio E. Unilateral games A fifth category of situations, which we term unilateral games, is characterized by the fact that each player has a dominant strategy that will be undertaken, independently from what the other player does, and these dominant strategies are different for the two players. In such games, the pay off matrix may take the following form For now, we are ignoring the possibility of Kashmir as an independent country, so that neither India nor Pakistan claim it. Of course, it is possible to convert this into a non-zero sum game, by including the costs incurred by each state in maintaining the conflict into the pay-off matrix. In this particular case, these costs are not insignificant. India and pakistan have fought two full scale wars, in 1948 and 1965 over the issue have had a major military encounter in 1999, and have had ongoing skirmishes for over fifty years. In addition, India claims that Pakistan is funding the ongoing insurgency, which India has had to fight. And these are only the direct military costs of the conflict. For an account of the 1948 and 1965 wars from the Indian perspective see JASWANT SINGH DEFENDING INDIA(1999)at 142, 155-160, 172-180. For an Indian journalists account of the 1999 military encounter, see SRINJOY CHOWDHURY, DESPATCHES FROM KARGIL(2000) 19 Indeed, all situations of conflict over a fixed resource are zero-sum games This pay-off matrix is inspired by robertO Keohane, Reciprocity in International Relations, 40 INT'L ORGN,1(1986
18For now, we are ignoring the possibility of Kashmir as an independent country, so that neither India nor Pakistan claim it. Of course, it is possible to convert this into a non-zero sum game, by including the costs incurred by each state in maintaining the conflict into the pay-off matrix. In this particular case, these costs are not insignificant. India and Pakistan have fought two full scale wars, in 1948 and 1965 over the issue; have had a major military encounter in 1999; and have had ongoing skirmishes for over fifty years. In addition, India claims that Pakistan is funding the ongoing insurgency, which India has had to fight. And these are only the direct military costs of the conflict. For an account of the 1948 and 1965 wars from the Indian perspective see JASWANT SINGH, DEFENDING INDIA (1999) at 142, 155-160,172-180. For an Indian journalist’s account of the 1999 military encounter, see SRINJOY CHOWDHURY, DESPATCHES FROM KARGIL (2000). 19 Indeed, all situations of conflict over a fixed resource are zero-sum games. 20This pay-off matrix is inspired by Robert O. Keohane, Reciprocity in International Relations, 40 INT’L ORG’N, 1(1986). 12 Kashmir. This is the quintessential zero-sum game - the territory can go to only one country.18 The gain to one country is exactly equal to the loss to the other, since the territory is available in a fixed amount.19 There is no way the winner can compensate the loser; there is no potential gain from mutual cooperation and, consequently, here is no role for reciprocity constraints in such a situation. E. Unilateral Games A fifth category of situations, which we term unilateral games, is characterized by the fact that each player has a dominant strategy that will be undertaken, independently from what the other player does, and these dominant strategies are different for the two players. In such games, the payoff matrix may take the following form:20
A4,2|R,4 p,2 I2,0 Figure(6): Unilateral Game Payoff In this case, Player A will always prefer Strategy I, regardless of Player B's strategy The interesting feature of such games is that a reciprocity constraint is actually undesirable from the perspective for maximizing the total payoff. With a reciprocity constraint, the possible payoffs are confined to the diagonal. But the outcome that maximizes social gain by maximizing total payoff is when Player A follows Strategy I and Player B uses Strategy Ill. With a reciprocity constraint, the best the players can do is use Strategy I, with a total payoff of 6. Without a reciprocity constraint
13 Figure (6): Unilateral Game Payoff In this case, Player A will always prefer Strategy I, regardless of Player B’s strategy The interesting feature of such games is that a reciprocity constraint is actually undesirable from the perspective for maximizing the total payoff. With a reciprocity constraint, the possible payoffs are confined to the diagonal. But the outcome that maximizes social gain by maximizing total payoff is when Player A follows Strategy I and Player B uses Strategy III. With a reciprocity constraint, the best the players can do is use Strategy I, with a total payoff of 6. Without a reciprocity constraint
the players could move to cell [I, Ill], with a total payoff of 8. In this case, social welfare is maximized by not imposing a reciprocity constraint. This is not a trivial or theoretical example; such behavior is often found in realm of international trade liberalization, as shown by robert Keohane But reciprocity constraints can be useful in multilateral trade negotiations, as many of the parties are not small countries 22 III IK4,23,4|2,6 I3,12 I2,0 Figure(7): Unilateral Game Payof with Reciprocity 2 See Keohane supra note 20. Unilateral trade liberalization can benefit a"small "country, by reducing costs to its consumers and producers, and therefore permitting a more efficient allocation of resources. A"small country is one that cannot influence world prices for any good or service by adjusting its own demand or supply generally PAUL R. KRUGMAN and MAURICE OBSTFELD, INTERNATIONAL ECONOMICS, THEORY AND POLICY, (5th 2000). Thus, a small country could benefit by reducing its own barriers of trade rather than engaging in import compression. See Nita Ghei and Lant Pritchett, The Three Pessimisms: Real Exchange Rates and Trade Flows in Developing Countries in LAWRENCE E HINKLE AND PETER J MONTIEL(EDS )EXCHANGE RATE MISALIGNMENT CONCEPTS AND MEASUREMENT FOR DEVELOPING COUNTRIES (1999) 2See discussion infra Part IL.B
21See Keohane supra note 20. Unilateral trade liberalization can benefit a “small” country, by reducing costs to its consumers and producers, and therefore permitting a more efficient allocation of resources. A “small” country is one that cannot influence world prices for any good or service by adjusting its own demand or supply. See generally PAUL R. KRUGMAN and MAURICE OBSTFELD, INTERNATIONAL ECONOMICS, THEORY AND POLICY, (5th ed. 2000). Thus, a small country could benefit by reducing its own barriers of trade rather than engaging in import compression. See Nita Ghei and Lant Pritchett, The Three Pessimisms: Real Exchange Rates and Trade Flows in Developing Countries in LAWRENCE E. HINKLE AND PETER J. MONTIEL (EDS.) EXCHANGE RATE MISALIGNMENT: CONCEPTS AND MEASUREMENT FOR DEVELOPING COUNTRIES (1999). 22See discussion infra Part III.B. 14 the players could move to cell [I, III], with a total payoff of 8. In this case, social welfare is maximized by not imposing a reciprocity constraint. Thisis not a trivial or theoretical example;such behavior is often found in realm of international trade liberalization, asshown byRobert Keohane.21 But reciprocity constraints can be useful in multilateral trade negotiations, as many of the parties are not small countries.22 Figure (7): Unilateral Game Payoff with Reciprocity