CUSTOMARY INTERNATIONAL LAW according to their self-interest. Although an observer might applaud the outcome because the states refrain from belligerence, the tcome is no more surprising than the fact that states do not sink ir own ships. States independently pursuing their own interests will engage in symmetrical or identical actions which do not cause harm to anyone, simply because the states gain nothing by deviating from those actions 2. Coercion A second type of strategic position in which states find themselves can be called coercion. One state. or a coalition of states with convergent interests, force other states to engage in actions that serve the interest of the first state or states To understand this strategic situation, imagine a game in which a large and powerful state initially can threaten to punish (or not) any small state that engages in any action X. The small state then chooses whether to engage in the action or not, and the large state responds by punishing the small state or not. The game then repeats itself. The large state receives its highest payoff if the small state does not engage in X, and the cost of punishing the small state is trivial. The small state receives a higher payoff if it does not engage in X and is not punished, than if it does engage in X and is punished. In equilibrium the large state makes the threat, the small state does not engage in X, and the large state does not punish the small state. The all state does not deviate because the large state would punish it if it did. If the small state did deviate the large state would punish the small state, because the cost of punishment is low and otherwise the large state's threats would have no effect on behavior in future ToU maintenance of the status quo rather than "mutual gains"except in the most attenuated sense 43 This game is based on models of entry deterrence in industrial organization.In those models, a firm or entrepreneur must decide whether to enter a market dominated by a monopolist, then the monopolist must decide whether to retaliate by cutting prices and expanding production. Several different models show that the monopolist can deter entry either by making a credible threat that it will cut prices or by in fact cutting prices prior to entry In the simplest model, which we use in the text, the monopolist cuts prices after entry in order to show future entrants that it will retaliate. In another model, some monopolists are irrational (or
15 CUSTOMARY INTERNATIONAL LAW according to their self-interest. Although an observer might applaud the outcome because the states refrain from belligerence, the outcome is no more surprising than the fact that states do not sink their own ships. States independently pursuing their own interests will engage in symmetrical or identical actions which do not cause harm to anyone, simply because the states gain nothing by deviating from those actions. 2. Coercion A second type of strategic position in which states find themselves can be called coercion. One state, or a coalition of states with convergent interests, force other states to engage in actions that serve the interest of the first state or states. To understand this strategic situation, imagine a game in which a large and powerful state initially can threaten to punish (or not) any small state that engages in any action X. The small state then chooses whether to engage in the action or not, and the large state responds by punishing the small state or not. The game then repeats itself. The large state receives its highest payoff if the small state does not engage in X, and the cost of punishing the small state is trivial. The small state receives a higher payoff if it does not engage in X and is not punished, than if it does engage in X and is punished. In equilibrium the large state makes the threat, the small state does not engage in X, and the large state does not punish the small state. The small state does not deviate because the large state would punish it if it did. If the small state did deviate, the large state would punish the small state, because the cost of punishment is low and otherwise the large state’s threats would have no effect on behavior in future rounds.43 maintenance of the status quo rather than “mutual gains” except in the most attenuated sense. 43 This game is based on models of entry deterrence in industrial organization. In those models, a firm or entrepreneur must decide whether to enter a market dominated by a monopolist, then the monopolist must decide whether to retaliate by cutting prices and expanding production. Several different models show that the monopolist can deter entry either by making a credible threat that it will cut prices or by in fact cutting prices prior to entry. In the simplest model, which we use in the text, the monopolist cuts prices after entry in order to show future entrants that it will retaliate. In another model, some monopolists are irrational (or
CHICAGO WORKING PAPER IN LAW AND ECONOMICS As an example, suppose that state i, a large and powerful nation, wishes to prevent small state j from king is civilian fishing boats. State i threatens state j by announcing that if state j does not stop its attacks, state i will destroy js navy. If state i cares enough about preventing j,'s attacks, and the cost of punishing state j is low enough, state i's threat will be credible, and state j will cease attacking the fishing vessels. If, for its own reasons, state i does not attack state js fishing boats, then observers will perceive a behavioral regularity consisting of states i and j not attacking each other's civilian fishing boats. They may conclude that a rule of CIL prohibits the seizure of fishing boats. But this harmonious result is produced by force. 44 Indeed, the application of force is more obvious when the weak party is passive. For example, state i might seize colonies of state j and threaten j with destruction if j resists Observers might hesitate about calling the outcome a norm of CIL, but the structure of the game is identical to that of the first example Coercion and coincidence of interest differ according to the degree to which a state's best action depends on the action of the other state. Coincidence of interest exists when a state's best action is independent of the action of the other state. Coercion exists when the weak state's best action depends on the strong states action, and the strong state would punish the weak state if the weak state chose the action that does not maximize the strong state's payoff prone to bad judgment) and others are rational; irrational monopolists retaliate by cutting prices in the second period, while rational monopolists mimic the irrational monopolist in order to deter future entrants. In a signaling model, the entrant does not know whether the monoplist has high or low costs, and the low-cost monopolist signals its low costs by charging low prices. In international relations, the analogies would be () powerful states sometimes being spiteful or irrational, and attacking weak states that do not do their bidding even though the cost of attacking them exceeds the benefit of successful coercion in a single round; or(ii) ome powerful states having cheaper militaries than others, and occasionally engaging in gratuitous displays of military might in order to reveal this private information to weaker countries. For discussions of the predatory pricing literature, see Baird et al., supra note at 178-86, and Jean Tirole, The Theory of Industrial Organization 367-74 (1997) 44 Alternatively, the large state might promise to give money to the small state if it stops seizing fishing boats. The strategic structure of the game is the sam whether the large state makes a threat or offers a bribe the difference being whether the outcome for the small state is better or worse than the status quo
CHICAGO WORKING PAPER IN LAW AND ECONOMICS 16 As an example, suppose that state i, a large and powerful nation, wishes to prevent small state j from attacking i’s civilian fishing boats. State i threatens state j by announcing that if state j does not stop its attacks, state i will destroy j’s navy. If state i cares enough about preventing j’s attacks, and the cost of punishing state j is low enough, state i’s threat will be credible, and state j will cease attacking the fishing vessels. If, for its own reasons, state i does not attack state j’s fishing boats, then observers will perceive a behavioral regularity consisting of states i and j not attacking each other’s civilian fishing boats. They may conclude that a rule of CIL prohibits the seizure of fishing boats. But this harmonious result is produced by force.44 Indeed, the application of force is more obvious when the weak party is passive. For example, state i might seize colonies of state j and threaten j with destruction if j resists. Observers might hesitate about calling the outcome a norm of CIL, but the structure of the game is identical to that of the first example. Coercion and coincidence of interest differ according to the degree to which a state’s best action depends on the action of the other state. Coincidence of interest exists when a state’s best action is independent of the action of the other state. Coercion exists when the weak state’s best action depends on the strong state’s action, and the strong state would punish the weak state if the weak state chose the action that does not maximize the strong state’s payoff. prone to bad judgment) and others are rational; irrational monopolists retaliate by cutting prices in the second period, while rational monopolists mimic the irrational monopolist in order to deter future entrants. In a signaling model, the entrant does not know whether the monoplist has high or low costs, and the low-cost monopolist signals its low costs by charging low prices. In international relations, the analogies would be (i) powerful states sometimes being spiteful or irrational, and attacking weak states that do not do their bidding even though the cost of attacking them exceeds the benefit of successful coercion in a single round; or (ii) some powerful states having cheaper militaries than others, and occasionally engaging in gratuitous displays of military might in order to reveal this private information to weaker countries. For discussions of the predatory pricing literature, see Baird et al., supra note __ at 178-86, and Jean Tirole, The Theory of Industrial Organization 367-74 (1997). 44 Alternatively, the large state might promise to give money to the small state if it stops seizing fishing boats. The strategic structure of the game is the same whether the large state makes a threat or offers a bribe, the difference being whether the outcome for the small state is better or worse than the status quo
CUSTOMARY INTERNATIONAL LAW 3.C The third basic type of strategic position in which states find themselves is that of the bilateral repeat prisoner's dilemma. Table 2 illustrates one stage of such a game Table 2 attack ignore attack 2,2 4,1 ignore 3,3 Consider the differences between this example and the coincidence of interest example. With coincidence of interest the state incurs a cost of 1 in order to attack fishing vessels and gains nothing. Here, the state incurs a cost of l and gains 2, while a state loses 2 if it is attacked. The coincidence of interest situation might correspond to modern conditions, when it is costly to operate a navy and the gains from seizing an enemy s civilian fishing boats are quite low, because they are worth very little as prizes or as means for disrupting the enemys economy. The prisoner's dilemma example might correspond to conditions under which it is not so costly to operate a navy and fishing boats are valuable or play an important role in the enemys economy. The analysis of this example is familiar State i obtains a higher payoff from seizing state j's fishing boats, regardless of whether state j also seize state i's boats(2>1)or not (4>3). State j's payoffs are symmetrical. Therefore, if Table 2 describes the whole game, and there is no possibility of future action or international sanctions, both states will seize the fishing boats of the other, and the jointly minimizing outcome is obtained As is well known, when the prisoner's dilemma is repeated over an indefinite period of time, the optimal outcome(ignore, ignore) in our case) becomes possible in each round. 45 Thus, one might hypothesize that each state will ignore the other state's fishing boats as long as the states expect to interact with each other over time. If 45 See standard game theory texts such as Baird et al., supra note, and Robert Gibbons, Game Theory for Applied Economists 82-99(1992)
17 CUSTOMARY INTERNATIONAL LAW 3. Cooperation The third basic type of strategic position in which states find themselves is that of the bilateral repeat prisoner’s dilemma. Table 2 illustrates one stage of such a game. Table 2 attack ignore attack 2, 2 4, 1 ignore 1, 4 3, 3 Consider the differences between this example and the coincidence of interest example. With coincidence of interest the state incurs a cost of 1 in order to attack fishing vessels and gains nothing. Here, the state incurs a cost of 1 and gains 2, while a state loses 2 if it is attacked. The coincidence of interest situation might correspond to modern conditions, when it is costly to operate a navy and the gains from seizing an enemy’s civilian fishing boats are quite low, because they are worth very little as prizes or as means for disrupting the enemy’s economy. The prisoner’s dilemma example might correspond to conditions under which it is not so costly to operate a navy and fishing boats are valuable or play an important role in the enemy’s economy. The analysis of this example is familiar. State i obtains a higher payoff from seizing state j’s fishing boats, regardless of whether state j also seize state i’s boats (2>1) or not (4>3). State j’s payoffs are symmetrical. Therefore, if Table 2 describes the whole game, and there is no possibility of future action or international sanctions, both states will seize the fishing boats of the other, and the jointly minimizing outcome is obtained. As is well known, when the prisoner’s dilemma is repeated over an indefinite period of time, the optimal outcome ((ignore, ignore) in our case) becomes possible in each round.45 Thus, one might hypothesize that each state will ignore the other state’s fishing boats as long as the states expect to interact with each other over time. If 45 See standard game theory texts such as Baird et al., supra note __, and Robert Gibbons, Game Theory for Applied Economists 82-99 (1992)
CHICAGO WORKING PAPER IN LAW AND ECONOMICS 18 they do so, the resulting equilibrium might be described as a norm of CIL. But many conditions must be satisfied before this result can be achieved irst, the players must have sufficiently low discount rates: they care about the future relative to the present. 47 Individuals who are impulsive or impatient or who do not care about the future have high discount rates. Such individuals cannot cooperate in an iterated prisoner,'s dilemma because they cannot resist cheating in round n, rather than in round n+l, so their threat to punish the other party in round n+1 if the latter cheats in round n is not credible. The international analogy to the impulsive individual is the rogue state. Rogue states are states controlled by irrational or impulsive leaders or states with unstable political systems, or states in which citizens do not enjoy stable expectations. Such states can be modeled having high discount rates. Ordinary states will not cooperate with rogue states for the same reason that disciplined individuals do not cooperate with impulsive individuals: they do not trust them Second, the game must continue indefinitely, in the sense that players expect it either never to end or to end only with a sufficiently low probability. 48 Care should be taken when analyzing the parameters of a game. Norms of war(such as the humane treatment of prisoners) might exist because (a) belligerents foresee interaction ceasing at the end of the war but do not know when the war will end, and refrain from"cheating"during the war(such as killing prisoners) in the expectation that the enemy will do the same;(b) belligerents foresee interaction continuing after the war ends, and fear that"cheating"during the war may invite retaliation after the 46 The conditions examined in the paragraphs that follow are standard in the game theory literature. For more detailed discussions, see Baird et al, supra note at 165-78: Morrow, supra note_, at 260-79 47 Discount rate refers to the degree to which a person prefers current payoffs to future payoffs. Suppose a person expects to receive $100 in one year. A person with a high discount rate of, say, 0.5 is indifferent between that amount in one year and about s67 today. a person with a low discount rate of, say, 0.1 is indifferent between that amount in one year and about $91 today. See gibbons, supra note_ at 68-69 n.7. 48 In more sophisticated analyses, this is not required: it is sufficient if players believe the game will not end for a long time and there is a small probability that a player is irrational or will make an error. See Morrow, supra note_ at 283-91
CHICAGO WORKING PAPER IN LAW AND ECONOMICS 18 they do so, the resulting equilibrium might be described as a norm of CIL. But many conditions must be satisfied before this result can be achieved.46 First, the players must have sufficiently low discount rates: they care about the future relative to the present.47 Individuals who are impulsive or impatient or who do not care about the future have high discount rates. Such individuals cannot cooperate in an iterated prisoner’s dilemma because they cannot resist cheating in round n, rather than in round n+1, so their threat to punish the other party in round n+1 if the latter cheats in round n is not credible. The international analogy to the impulsive individual is the rogue state. Rogue states are states controlled by irrational or impulsive leaders, or states with unstable political systems, or states in which citizens do not enjoy stable expectations. Such states can be modeled as having high discount rates. Ordinary states will not cooperate with rogue states for the same reason that disciplined individuals do not cooperate with impulsive individuals: they do not trust them. Second, the game must continue indefinitely, in the sense that players expect it either never to end or to end only with a sufficiently low probability.48 Care should be taken when analyzing the parameters of a game. Norms of war (such as the humane treatment of prisoners) might exist because (a) belligerents foresee interaction ceasing at the end of the war but do not know when the war will end, and refrain from “cheating” during the war (such as killing prisoners) in the expectation that the enemy will do the same; (b) belligerents foresee interaction continuing after the war ends, and fear that “cheating” during the war may invite retaliation after the 46 The conditions examined in the paragraphs that follow are standard in the game theory literature. For more detailed discussions, see Baird et al, supra note __, at 165-78; Morrow, supra note __, at 260-79. 47 Discount rate refers to the degree to which a person prefers current payoffs to future payoffs. Suppose a person expects to receive $100 in one year. A person with a high discount rate of, say, 0.5 is indifferent between that amount in one year and about $67 today. A person with a low discount rate of, say, 0.1 is indifferent between that amount in one year and about $91 today. See Gibbons, supra note __ at 68-69 n.7. 48 In more sophisticated analyses, this is not required: it is sufficient if players believe the game will not end for a long time and there is a small probability that a player is irrational or will make an error. See Morrow, supra note __ at 283-91
CUSTOMARY INTERNATIONAL LAW war;or(c)belligerents care about their reputation among neutrals, and fear that neutrals will interpret their failure to abide by the norms of war as an indication that they have low discount rates and thus are untrustworthy partners for alliances. This last possibility requires a more complicated model, and we will analyze such a model in Section II.C. For present purposes, it is sufficient to note that analysis of customs between states, such as their treatment of each other's civilian fishing vessels, should not overlook the influence of future interaction between the states outside the narrow context of the to l hird, the payoffs from defection must not be too high relative he payoffs from cooperation. Notice that because payoffs may change over time, a relationship may succeed for a while and then, after a sudden change in payoffs, collapse. Imagine two neighboring states that do not seize each other's fishing boats in a repeat game characterized by stage games with the payoffs described in Table 2 State i receives(2+d2 +d 2 +. from cooperating, which exceeds the payoff from cheating on the first round assuming that State plays the"grim strategy and retaliates by refusing to cooperate in all future rounds(4+0+0+., given a sufficiently high d, where d refers to the discount factor. 49 Suppose that because of an exogenous change the one-time payoff from cheating rises to 100. Then, given he right d, State i will cheat rather than cooperate, and State j will retaliate by cheating. Cooperation disappears Fourth, players must choose sufficiently cooperative strategies, such as tit-for-tat or a variant Strategies that are too forgiving invite exploitation; strategies that are too nasty risk a breakdown in cooperation. If states initially choose strategies randomly, and then less successful states imitate the strategies of more successful states, then it is plausible that over time the better strategies will drive out the worse strategies. 50 Fifth, the action that will overcome the prisoner's dilemma must be clear, and identical or symmetrical. Not seizing fishing vessels is clear and identical for both states. If, however, the optimal action were seizing fishing vessels 32 percent of the time, the action would 49 If r is the discount rate, d=1/(1+r). See Gibbons, supra note_at68-69n7 50 See Axelrod, supra note
19 CUSTOMARY INTERNATIONAL LAW war; or (c) belligerents care about their reputation among neutrals, and fear that neutrals will interpret their failure to abide by the norms of war as an indication that they have low discount rates and thus are untrustworthy partners for alliances. This last possibility requires a more complicated model, and we will analyze such a model in Section II.C. For present purposes, it is sufficient to note that analysis of customs between states, such as their treatment of each other’s civilian fishing vessels, should not overlook the influence of future interaction between the states outside the narrow context of the game. Third, the payoffs from defection must not be too high relative to the payoffs from cooperation. Notice that because payoffs may change over time, a relationship may succeed for a while and then, after a sudden change in payoffs, collapse. Imagine two neighboring states that do not seize each other’s fishing boats in a repeat game characterized by stage games with the payoffs described in Table 2. State i receives (2 + d2 + d2 2 + ...) from cooperating, which exceeds the payoff from cheating on the first round assuming that State j plays the “grim” strategy and retaliates by refusing to cooperate in all future rounds (4 + 0 + 0 + ...), given a sufficiently high d, where d refers to the discount factor.49 Suppose that because of an exogenous change the one-time payoff from cheating rises to 100. Then, given the right d, State i will cheat rather than cooperate, and State j will retaliate by cheating. Cooperation disappears. Fourth, players must choose sufficiently cooperative strategies, such as tit-for-tat or a variant. Strategies that are too forgiving invite exploitation; strategies that are too nasty risk a breakdown in cooperation. If states initially choose strategies randomly, and then less successful states imitate the strategies of more successful states, then it is plausible that over time the better strategies will drive out the worse strategies.50 Fifth, the action that will overcome the prisoner’s dilemma must be clear, and identical or symmetrical. Not seizing fishing vessels is clear and identical for both states. If, however, the optimal action were seizing fishing vessels 32 percent of the time, the action would 49 If r is the discount rate, d=1/(1+r). See Gibbons, supra note __ at 68-69 n.7. 50 See Axelrod, supra note __