Deliberational Dynamics and The Foundations of Bayesian Game Theory

1. Introduction: There are two rationality concepts at work in separate areas of the theory of rational decision: EQUILIBRIUM, which is the dominant solution concept in the theory of noncooperative games and MAXIMUM EXPECTED UTILITY which is the central principle in the theory of coherent individual choice under uncertainty. In the development of game theory, the relationship between the two principles, and to a lesser extent the status of the equilibrium principle itself, has been less than crystal clear.2 This question is put in a new light if we regard deliberation as a dynamical process with informational feedback. We will take the expected utility principle as basic. One deliberates by calculating expected utility. In the simplest cases deliberation is trivial; one calculates expected utility and maximizes. But in more interesting cases, the very process of deliberation may generate information which is salient to the evaluation of the expected utilities. Then, processing costs permitting, a Bayesian deliberator will feedback that information and recalculate the expected utilities in light of the new knowledge.3 In such an interesting decision problem, deliberation can be modeled as a dynamic system. The decision maker starts in a state of indecision; calculates expected utility; moves in the direction of maximum expected utility; feeds back the information generated and recalculates; etc. In this process, his probabilities of doing the various acts evolve4 until, at the time of decision, his probabilities of doing the selected act become virtually one.