19 Expected Utility as a Tool in Non - Cooperative Game Theory

This sequel to previous chapters on objective and subjective expected utility reviews conditions for players in a non-cooperative game to be Bayesian rational — i.e., to choose a strategy maximizing the expectation of each von Neumann–Morgenstern utility function in a unique cardinal equivalence class. In classical Nash equilibrium theory, players’ mixed strategies involve objective probabilities. In the more recent rationalizability approach pioneered by Bernheim and Pearce, players’ possibly inconsistent beliefs about other players’ choices are described by unique subjective probabilities. So are their beliefs about other players’ beliefs, etc. Trembles, together with various notions of perfection and properness, are seen as motivated by the need to exclude zero probabilities from players’ decision trees. The work summarized here, however, leaves several foundational issues unsatisfactorily resolved.