Game theory has proved a useful tool in the study of simple economic models. However, numerous foundational issues remain unresolved. The situation is particularly confusing in respect of the non-cooperative analysis of games with some dynamic structure in which the choice of one move or another during the play of the game may convey valuable information to the other players. Without pausing for breath, it is easy to name at least 10 rival equilibrium notions for which a serious case can (...) be made that here is the “right” solution concept for such games. (shrink)

This book explores how individual actions coordinate to produce unintended social consequences. In the past this phenomenon has been explained as the outcome of rational, self-interested individual behaviour. Professor Bicchieri shows that this is in no way a satisfying explanation. She discusses how much knowledge is needed by agents in order to coordinate successfully. If the answer is unbounded knowledge, then a whole variety of paradoxes arise. If the answer is very little knowledge, then there seems hardly any possibility of (...) attaining coordination. The solution to coordination and cooperation is for agents to learn about each other. The author concludes that rationality must be supplemented by models of learning and by an evolutionary account of how social order can persist. (shrink)

For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1.

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines, all of whom are engaged in research at the forefront of their fields. Together they offer a conspectus of the interaction of game theory, logic and epistemology in the formal models of (...) knowledge, belief, deliberation and learning, and in the relationship between Bayesian decision theory and game theory, as well as between bounded rationality and computational complexity. (shrink)

Gian Aldo Antonelli and Cristina Bicchieri. Forward Induction.