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- Cristina Bicchieri (1988). Strategic Behavior and Counterfactuals. Synthese 76 (1):135 - 169.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.
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It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one for each player, such that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a..
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