Correlated equilibria and the dynamics of rational deliberation

Abstract

De Finetti and Ramsey showed how rational decision is founded on coherence. This should be true in game theoretic contexts just as much as in other ones. If followed to their logical conclusion considerations of coherence can lead to dynamic deliberation and in this context introduce a natural Bayesian equilibrium concept. Such deliberational equilibria are intimately connected with game theoretic equilibria in games played by Bayesian deliberators. 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 relevant to the evaluation of the expected utilities.2 Then, processing costs permit? ting, a Bayesian deliberator will feedback that information and recal? culate 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 max? imum expected utility; feeds back the information generated and recalculates; etc. In this process, his probabilities of doing the various acts evolve until, at the time of decision, his probabilities of doing the selected act become virtually one. Dynamic deliberation carries with it an equilibrium principle for individual decision. The decision maker cannot decide to do an act