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 addressing 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.
1Welfare 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...