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Published online by Cambridge University Press: 18 March 2010
Game theory is a rich field for the philosopher. It formulates principles of rational action and so makes immediate contributions to the branch of logic that studies practical reasoning. Its principles of strategic reasoning also provide the undergirding for the social contract theory and the study of social and linguistic convention. Revisions of central game-theoretic tenets reverberate throughout philosophy.
This book makes some assumptions about rationality and equilibrium in games and traces out their consequences. These are the main assumptions: (1) There are no dilemmas of rationality; an agent has a rational choice in every choice situation. (2) Every ideal game has a solution, that is, a profile of jointly rational strategies. (3) A rational choice is self-supporting. (4) An equilibrium is a profile of strategies that are jointly self-supporting. These assumptions suggest replacing Nash equilibrium, which fails to exist in some ideal games, with a new type of equilibrium called strategic equilibrium. Strategic equilibrium is introduced via a study of self-support. Taking an equilibrium to be a profile of jointly self-supporting strategies, I use a new account of self-support to obtain the new type of equilibrium. I show that a strategic equilibrium exists in every ideal normal-form game meeting certain mild restrictions and provide procedures for finding strategic equilibria in those games.
This project arose from reflections on cooperative games, where individuals may form coalitions that adopt joint strategies and otherwise act as agents. I took being an equilibrium as a necessary condition for being a solution to a cooperative game, and this led to a problem.
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