Expected Utility in Non-Cooperative Game Theory

Abstract

The theory of equilibrium in general non-cooperative games was initially developed for two-person ``zero-sum'' games by Borei (1921, 1924), von Neumann (1928) and von Neumann and Morgenstern (1944).1 It was then extended to general n-person games with finite strategy sets by Nash (1950, 1951). This classical theory allows different players to choose stochastically independent ``mixed'' strategies in the form of objective probability distributions. In this connection, Aumann (1987b, p. 466) gives a very clear and concise account of the role played by objectively expected utility theory in the classical theory of games with independent mixed strategies. A recent extension of classical non-cooperative game theory due to Aumann (1974, 1987a) allows different players to correlate their mixed strategies through some form of correlation device.2