Game Theory and its Relation to Bayesian Theory

Abstract

Bayesian decision theory and traditional Game Theory share a common decision rule—maximizing expected utility—in decisions under risk—where the problem includes a well defined probability for all states of affairs. However, in decisions under uncertainty—where no such probability is given by the problem, which includes traditional problems of game theory—Game Theory insists that rational players satisfy an equilibrium criterion instead. Strategies for different players form a (Nash) equilibrium when, simultaneously, each is a best reply against the strategies adopted by the opponent(s). This article illustrates several specialized circumstances where Bayesian theory advocates an equilibrium solution. However, the more general setting is one where Bayesian theory does not privilege the Nash equilibrium. Variations and refinements of the traditional Nash equilibrium criterion are considered in mitigation of this tension with Bayesian expected utility theory.