Collective rationality in its ordinary sense is rationality's extension to groups. It does not entail efficiency by definition. Showing that it entails efficiency requires a normative argument. Game theorists treating cooperative games generally assume that collective rationality entails efficiency, but formulating the reasoning that leads individuals to efficiency, and verifying the rationality of its steps, presents challenging philosophical issues. This paper constructs a framework for

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... sing those issues and reaches some preliminary results about the prospects of rational agents achieving efficiency in coalitional games. It concludes that only under strong idealizations does collective rationality entail efficiency. 1 Welfare economics formulates idealizations, such as perfect competition, under which markets yield efficient allocations of goods. In a similar spirit, this essay formulates idealizations under which efficiency emerges in coalitional games. These are games in which players may form coalitions and act jointly. Many theorists propose the standard of efficiency for solutions to cooperative games, including coalitional games, and so suggest that collectively rational players achieve an efficient outcome. 1 However, this essay finds that in a coalitional game, the players' collective rationality in its ordinary sense does not ensure efficiency even if the game satisfies standard idealizations. The essay therefore strengthens standard idealizations to make collective rationality generate efficiency. To obtain efficiency, it adds the idealization that players rationally prepare for their game. The first section explains why, in coalitional games, collectively rational players may not achieve efficiency. It describes collective rationality and efficiency, and shows that although collective rationality aims for efficiency, obstacles often prevent its attainment. The second section examines collective rationality's requirement that players achieve a solution in a coalitional game. A solution assigns strategies to players so that the strategies are jointly rational, and consequently form an equilibrium among players' incentives. So that equilibrium is attainable, this section takes equilibrium as strategic equilibrium, a type of equilibrium that does not require all players to pursue all incentives-that is impossible in some coalitional games. It requires only that players pursue compelling incentives. Players who meet this equilibrium standard may not achieve efficiency, however. So collective rationality's requiring a solution does not in general ensure efficiency. The final section shows that a coalitional game's solution yields an efficient outcome if the players rationally prepare for their game. Prior to their game, fully rational players coordinate their pursuit of incentives so that it ensures 1 See, for example, John von Neumann and Oskar Morgenstern (1944: Sec. 4) and John Nash (1950). 2 efficiency in the game. Because their rational preparation is a suitable idealization, collective rationality entails efficiency in thoroughly ideal conditions. The essay's argument that collective rationality entails efficiency in an ideal coalitional game shows first that in an ideal game collective rationality requires each individual's rationality, and shows next that the rationality of all individuals entails efficiency. It claims that fully rational individuals prepare for a coalitional game by coordinating their pursuit of incentives so that it yields an efficient outcome in the game. Collectively Rational Inefficiency This essay gives rationality its ordinary sense and so takes rationality to require more than instrumental rationality, or rationality in pursuit of goals. Rationality evaluates beliefs and goals, as well as means of pursuing goals given beliefs. However, the essay relies mainly on principles of rationality governing pursuit of goals, such as the principle to maximize expected utility, which addresses cases where probability and utility functions represent, respectively, beliefs and desires. For an ideal agent in a standard decision problem, an option is rational just in case it maximizes expected utility. Although this is not a general definition of rationality, it covers the decision problems this essay treats. The principle to maximize expected utility, formulated in a general way, governs decisions that players make in games, as Weirich (1998) argues. This section characterizes efficiency and collective rationality, examines obstacles to efficiency, and reviews idealizations that put aside some obstacles. Collective rationality aims at efficiency, and under suitable idealizations achieves efficiency, although standard idealizations do not ensure its success. Although efficiency may seem to be a requirement of collective irrationality, collectively rational groups may for various reasons fail to be efficient. Efficiency is a goal of collective rationality in the sense that in ideal conditions a group acting rationally achieves efficiency. basic principle of collective rationality, the pair's failure to cooperate is collectively rational. The players' inability to communicate and to reach binding agreements excuses the pair's inefficiency. Efficiency is a goal of collective rationality, but collectively rational players may not achieve that goal in adverse circumstances. Providing opportunities for communication and binding agreements improves the prospects that rational players will achieve efficiency. Changing the circumstances of the Prisoner's Dilemma by adding these opportunities creates a cooperative version of the game. Suppose that in it, the players know their situation and know they are rational. They realize that each is better off if both cooperate than if both defect. Neither thinks that the other will decline a binding contract for mutual cooperation. Given ideal conditions for joint action, one player proposes the contract and the other accepts it. Thus the pair cooperates. Suppose that to improve the prospects for efficiency in a cooperative game, we adopt the assumption that conditions are ideal for joint action. Besides opportunities for costless communication and binding contracts, agents are informed about their situation and each other. They know enough about their game and each other to have foreknowledge of their joint action. Strengthening the idealizations for cooperative games this way nonetheless fails to ensure efficiency. Approach.