In an ideal game each agent is ideal and ideally situated. The agents are rational, prescient, and informed about the game. These are strong idealizations, and much recent work in game theory is sensibly concerned with weakening them, especially the idealization of prescience. We keep the idealizations at full strength, however, because of their role in explications of important features of strategic reasoning. This chapter explains and motivates our idealizations.

THE CRITERION FOR IDEALIZATIONS

The agents in an ideal game decide rationally, have the power to anticipate each other, and have full knowledge of the payoff structure of the game and the circumstances of the agents. The foregoing is only a rough characterization of ideal games, however. It leaves unsettled some matters resolvable in ways that either support or undermine our claims about solutions and equilibria in ideal games. It is tempting to support or undermine those claims with stipulations about the features of ideal games, but this temptation should be resisted.

To support our claim that solutions exist in ideal games, it is tempting to stipulate that any game without a solution is not ideal. To undermine our claim that Nash equilibria are absent in some ideal games, it is tempting to stipulate that a game is ideal only if each agent is prescient, is informed about the game, and adopts an incentive-proof strategy. Since this condition is not met in games without Nash equilibria, such games would then be classified as nonideal.