1. For discussions of the interaction between sanctioning and monitoring problems, see Bendor, Jonathan, “In Good Times and Bad: Reciprocity in an Uncertain World,” American Journal of Political Science 31 (08 1987), pp. 531–58CrossRefGoogle Scholar; and George W., Downs and Rocke, David M., Tacit Bargaining, Arms Races, and Arms Control (Ann Arbor: University, of Michigan Press, 1990)Google Scholar.

2. My distinction between sanctioning and monitoring on one hand and distribution and information on the other parallels Stein's distinction between collaboration and coordination. Sanctioning and monitoring are problems of collaboration, and distribution and information are problems of coordination. See Stein, Arthur A., Why Nations Cooperate: Circumstance and Choice in International Relations (Ithaca, N.Y.: Cornell University Press, 1990)Google Scholar. Lisa Martin adds problems of suasion and assurance to Stein's two problems in “Interests, Power, and Multilateralism,” International Organization 46 (Autumn 1992), pp. 765–92CrossRefGoogle Scholar. The model here addresses both of Martin's problems. Suasion is a special case of coordination, and assurance is captured in the both-prefer games described below.

3. For discussions of some of the problems of reaching agreement on how to cooperate, seeKrasner, Stephen D., “Global Communications and National Power: Life on the Pareto Frontier,” World Politics 43 (04 1991), pp. 336–66CrossRefGoogle Scholar; and Sebenius, James K., “Challenging Conventional Explanations of International Cooperation: Negotiation Analysis and the Case of Epistemic Communities,” International Organization 46 (Winter 1992), pp. 323–365CrossRefGoogle Scholar.

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5. The work here draws heavily on work in economics on “cheap talk”—cost-free, nonbinding messages. See Farrell, Joseph, “Cheap Talk, Coordination, and Entry,” Rand Journal of Economics 19 (Spring 1987), pp. 34–39CrossRefGoogle Scholar; and Farrell, Joseph and Gibbons, Robert, “Cheap Talk Can Matter in Bargaining,” Journal of Economic Theory 48 (06 1989), pp. 221–37CrossRefGoogle Scholar. For a discussion of the signaling game framework and an analysis of how signals can aid cooperation, see Crawford, Vincent P. and Sobel, Joel, “Strategic Information Transmission,” Econometrica 50 (11 1982), pp. 1431–51CrossRefGoogle Scholar. For an analysis of how different forms of communication assist in coordination problems in which there is limited information, see Banks, Jeffrey S. and Calvert, Randall L., “A Battle-of-the-Sexes Game with Incomplete Information,” Games and Economic Behavior, vol. 4, no. 2, 1992, pp. 347–72CrossRefGoogle Scholar.

6. Schotter develops the view that social institutions, of which regimes are an example, are equilibria of a game. See Schotter, Andrew, The Economic Theory of Social Institutions (New York: Cambridge University Press, 1981)CrossRefGoogle Scholar.

7. For a discussion of diffuse reciprocity, see Keohane, Robert O., “Reciprocity in International Relations,” International Organization 40 (Winter 1986), pp. 1–27CrossRefGoogle Scholar.

8. See Haas, Ernst B., “Why Collaborate? Issue-Linkage and International Regimes,” World Politics 32 (04 1980), pp. 357–405CrossRefGoogle Scholar; Haas, Ernst B., “Words Can Hurt You; or, Who Said What to Whom About Regimes,” in Krasner, , International Regimes, pp. 23–59Google Scholar; and John Gerard Ruggie, “International Regimes, Transactions, and Change: Embedded Liberalism in the Postwar Economic Order,” in ibid., pp. 195–231.

9. See for example, Wendt, Alexander, “Anarchy is What States Make of It: The Social Construction of Power Politics,” International Organization 46 (Spring 1992), pp. 391–425CrossRefGoogle Scholar.

10. Codding, George A. Jr., The International Telecommunications Union: An Experiment in International Cooperation (Leiden: E.J. Brill, 1952), pp. 60–61Google Scholar.

11. Ibid., pp. 61–75.

12. If the actors must reach an agreement that will persist over time, agreement may be difficult in the face of distributional interests. Fearon shows that long “shadows of the future” make reaching such agreements more difficult. See Fearon, James, “Cooperation and Bargaining Under Anarchy,” paper presented at the annual meeting of the Public Choice Society, New Orleans, La., 19–21 03 1993Google Scholar.

13. See pp. 206–14 of Lipson, Charles, “Bankers' Dilemmas: Private Cooperation in Rescheduling Sovereign Debts,” in Oye, Kenneth A., ed., Cooperation Under Anarchy (Princeton, N.J.: Princeton University Press, 1986), pp. 200–225Google Scholar.

14. Haas, Peter M., “Do Regimes Matter? Epistemic Communities and Mediterranean Pollution Control,” International Organization 43 (Summer 1989), pp. 377–403CrossRefGoogle Scholar.

15. Kindleberger, Charles P., The World in Depression, 1929–1939, 2d ed. (Berkeley: University of California Press, 1986), pp. 288–305Google Scholar. Also see Snidal, Duncan, “The Limits of Hegemonic Stability Theory,” International Organization 39 (Autumn 1985), pp. 579–614CrossRefGoogle Scholar, for a critique of this view.

16. Similarly, externalities create distributional problems. The Coase theorem states that such problems can be resolved by private negotiation if property rights are already defined, and the actors have perfect information and do not face transaction costs. But the adoption of a property rights regime creates a distributional problem. Keohane discusses the Coase theorem and international cooperation in After Hegemony, pp. 85–87Google Scholar.

17. See Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984)Google Scholar. Prisoners' dilemma is the two-by-two game with a dominant strategy equilibrium, typically labeled D for “defect,” that is not Pareto-optimal. In single-shot play or iterated games with a fixed end point, D is the dominant strategy of the game on all rounds. The outcome produced by the other strategy, typically labeled C for “cooperate,” improves both players' payoff over DD.

18. Tit-for-tat is not a perfect equilibrium of the open-ended iterated prisoners' dilemma because it requires suboptimal behavior if one side defects; see Rasmusen, Eric, Games and Information (Cambridge: Basil Blackwell, 1989), p. 91Google Scholar. Actors are better off if they do not carry out the punishments dictated by tit-for-tat.

19. Axelrod, Robert and Keohane, Robert O., “Achieving Cooperation Under Anarchy: Strategies and Institutions,” in Oye, , Cooperation Under Anarchy, pp. 226–54Google Scholar.

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21. Luce, R. Duncan and Raiffa, Howard, Games and Decisions (New York: John Wiley, 1957), p. 91Google Scholar. Snidal and Stein each also argue that battle of the sexes exhibits elements of the problem of international cooperation that the prisoners' dilemma does not. see Snidal, Duncan, “Coordination Versus Prisoners' Dilemma: Implications for International Cooperation and Regimes,” American Political Science Review 79 (12 1985), pp. 923–42CrossRefGoogle Scholar; and Stein, Arthur A., “Coordination and Collaboration: Regimes in an Anarchic World,” in Krasner, , International Regimes, pp. 115–40Google Scholar, respectively.

22. I use the term “move” rather than “strategy” to describe each player's choice in a particular round. Strategies in game theory are complete plans to play the game. A strategy here specifies what moves should be played and what messages—if any—should be sent in any possible round. For an introduction to game theory, see Morrow, James D., Game Theory for Political Scientists (Princeton, N.J.: Princeton University Press, 1994)Google Scholar.

23. Alternatively, one can assume that the parties agree to a middle price halfway between the two prices if the buyer proposes a high price and the seller, a low price. This variation does not change the strategic logic of battle of the sexes. There are still two pure strategy equilibria, (A;A) and (B;B), and a symmetric mixed-strategy equilibrium. The probabilities of each move in the mixed-strategy equilibrium do change.

24. Keohane, , After Hegemony, p. 63Google Scholar.

25. Both-prefer games are also known as “stag hunt” or an assurance game; see Martin, “Interests, Power, and Multilateralism,” and Stein, Why Nations Cooperate.

26. The model is symmetric because all three games are symmetric. Both players have the same payoff for the three possible outcomes: more preferred coordination, less preferred coordination, and no coordination. This symmetry has no effect on the equilibria of the game, as I discuss later.

27. For a review of signaling games and their application to political science, see Banks, Jeffrey S., Signaling Games in Political Science (New York: Gordon and Breach, 1991)Google Scholar.

28. The symmetry of equal chances of each game being played and each signal does not influence the set of equilibria for the model. Changing these probabilities alters the mixed strategies in each equilibrium.

29. Haas, E., “Why Collaborate?” pp. 367–70Google Scholar.

30. Keohane adds that regimes assist cooperation by changing transaction costs to favor mutually beneficial trades. See After Hegemony, pp. 89–92.

31. See Friedman, James, “A Noncooperative Equilibrium for Supergames,” Review of Economic Studies 38 (01 1971), pp. 1–12CrossRefGoogle Scholar; and Fudenberg, Drew and Maskin, Eric, “The Folk Theorem in Repeated Games with Discounting or with Incomplete Information,” Econometrica 54 (05 1986), pp. 533–54CrossRefGoogle Scholar.

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33. I examine perfect Bayesian equilibria of the model. Actors act rationally at each move given their beliefs in a perfect Bayesian equilibrium; see Morrow, Game Theory for Political Scientists, chap. 6. In this model, the actors' beliefs are the probability of the game they are playing given the information the actor has at that moment. Sequential rationality requires that the actors' messages and moves are optimal given their beliefs when those messages are sent and moves made and that their beliefs are calculated from their equilibrium strategies using Bayes's law whenever possible.

34. The model also has asymmetric equilibria without communication. In such an asymmetric equilibrium, the actors always coordinate on one move—A or B—leading to different expected payoffs. Because the game is symmetric, there is no a priori way to distinguish the players. Harsanyi and Selten argue that in the absence of any way to distinguish the players in a symmetric game, only symmetric equilibria are plausible; see Harsanyi, John C. and Selten, Reinhart, A General Theory of Equilibrium Selection in Games (Cambridge, Mass: MIT Press, 1988), pp. 70–71Google Scholar. I ignore the asymmetric equilibria of the game. Without some mechanism to explain how the players share mutual expectations that they will always play one move, we cannot explain how the players can play an asymmetric equilibrium. I discuss later a regime with communication that produces asymmetric payoffs for the players.

35. For specifications of all equilibria and proofs, please see the appendix.

36. By assuming that messages honestly report information unless the players have incentives to dissemble, I follow Rabin's concept of “credible message” equilibrium; see Rabin, Matthew, “Communication Between Rational Agents,” Journal of Economic Theory 51 (06 1990), pp. 144–70CrossRefGoogle Scholar. There are equilibria that mirror those discussed in the text, i.e., wherein the messages mean the opposite of the observed signal. As Rabin cogently argues, agents agree on forms of communication that can be used to refine the set of equilibria of a game. Equilibrium behavior depends not only on the incentives of the game but also on forms of communication between the players.

37. The pure coordination equilibrium is also preferable to the dishonest communicative equilibrium whenp < a/(3a – 2), which is greater than (a – l)/(3a + 1). A later section discusses choosing among different possible equilibria.

38. There are other ways to send messages sequentially that have the same effect. For example, the first player's message indicates what move the players will coordinate on unless the second player objects to that move in its response. In all cases, the second message provides the cue that the players use to coordinate.

39. The self-enforcing feature of battle of the sexes contrasts with prisoners' dilemma, in which players always have a short-run incentive to defect. General reciprocal punishment strategies also produce behavior that looks like Keohane's diffuse reciprocity. See Bendor, “In Good Times and Bad,” and Downs and Rocke, Tacit Bargaining, Arms Races, and Arms Control.

40. Keohane, , “Reciprocity in International Relations,” pp. 20–21Google Scholar.

41. In the leadership regime, there is no reciprocity for the follower. The follower does the leader's bidding because following the leader's directives is in its short-run interest. Still, the leadership equilibrium does produce an equal expected distribution of the total payoff when p > ½. This equality results because the follower denies the leader the information that the leader needs to exploit the follower.

42. Keohane, , After Hegemony, p. 59Google Scholar.

43. Lipson, “Bankers' Dilemmas.”

44. P. Haas, “Do Regimes Matter?”

45. For the claim that the “shadow of the future” is necessary for cooperation among egoists, see Axelrod, The Evolution of Cooperation.

46. Young, Oran R., “The Politics of International Regime Formation: Managing Natural Resources and the Environment,” International Organization 43 (Summer 1989), pp. 349–75 and specifically pp. 361–62 and 367CrossRefGoogle Scholar.

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50. Ibid., p. 571.

51. See E. Haas, “Why Collaborate?”; E. Haas, “Words Can Hurt You”; and Ruggie, “International Regimes, Transactions, and Change.”

52. Ruggie, , “International Regimes, Transactions, and Change,” p. 200Google Scholar.

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54. Krasner, Stephen D., “State Power and the Structure of International Trade,” World Politics 28 (04 1976), pp. 317–47CrossRefGoogle Scholar.

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56. Keohane, After Hegemony.

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60. Alt, Calvert, and Humes, “Reputation and Hegemonic Stability.”

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