It is a basic tenant for most of us that it is better to know something rather than nothing and to make informed decisions rather than uninformed ones. Professor Skyrms is examining the problem of how best to make decisions in a situation where the very process of deliberating about the decision generates new information which will allow us to make more informed decisions. In this dynamic deliberational process, decision makers start in a state where they are not at all certain what the best course of action should be; but by feeding back information from the deliberational process, the probabilities of doing various acts evolve until the final decision becomes clear. Such a study is focussed on questions in decision theory and game theory, but they have an important bearing upon issues in the policy sciences--for example, in debates about the best course of action in the arms race. Further, these results have important implications for the theory of scientific inference, that is on how science moves from particular instances or events to a generalizable theory which accurately describes the world about us. Professor Skryms is specifically examining the relationships of deliberational dynamics and Bayesian Game theory. Deliberational dynamics shows how the dominant solution concept of Game Theory, that of a Nash equilibrium, can be grounded on the expected utility principle of the theory of individual rational decision. Expected utility motivates dynamic deliberation, and a Nash equilibrium corresponds to a fixed point of the joint deliberational dynamics of the players of the game in question under ideal conditions of common knowledge. Professor Skyrms will investigate the stability of fixed points in the deliberational dynamics, and use this framework to throw light on the current discussions of refinements of the Nash equilibrium concept in both normal form and extensive form games. He will also investigate the results of weakening the strong common knowledge assumptions required in the foregoing with regard to both the initial state of indecision and the fact that all players of the game are Bayesian deliberators. He will show that minimal weakening of these assumptions can have dramatic effects on the possible rational solutions for games that are important in modeling real life decisions.
