Multiagent Bayesian theory and economic models of duopoly, R&D, and bank runs

Both Bayesian decision theory and game theory propose standards of rational behavior, and both are endorsed by modern economic theory. In Savage's Bayesian, view, the probability that a person assigns to a possible outcome or some process represents her own judgment of the likelihood that the outcome will be obtained. Most existing Bayesian game theory models sacrifice this subjective view of probability and are Bayesian only in some of the mechanics. Exceptions are the extension of Savage's approach to game contexts of Kadane and Larkey and a few other authors. In this chapter, we adhere to this subjective Bayesian approach and explore the type of subjective beliefs players must have about their opponents in order to play the solution concepts proposed by classical game theory in some specific well-studied noncooperative economic games: repeated duopoly, investment in R&D, and bank runs. We analyze the implications of the subjective approach for repeated games and equilibrium selection, although with this approach rational play does not necessarily imply equilibrium behavior. Cooperation in repeated duopoly appears in this theory not because of some ad hoc psychological concept but because the subjective beliefs of players lead to making cooperative decisions, The specific equilibrium that will result will be also determined by the beliefs of the players, not by some ad hoc definition of what optimal play should be. We propose that subjective Bayesian game theory helps in bridging the gap between empirical work and theoretical work that has plagued classical applied game theory.