Strategic Behavior and Counterfactuals
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{'SignBlockName': 'Alicia Armstrong', 'PO_EMAI': 'aarmstro@nsf.gov', 'PO_PHON': '7032924743'}
In game theory, the difficulty of defining rational behavior in game            situations like the prisoner's dilemma is the fact 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 being objectively correct, but no explanation             is offered of the mechanism generating this property of the belief              system.  In most cases, however, such a rationality requirement is              not enough to guarantee that an equilibrium will be attained.  Under            this research grant, Dr. Bicchieri is concentrating on the                      relationship between an assumption of epistemic rationality and                 equilibrium.  By equilibrium, she means a combination of actions such           that no agent would want to change his action if he were to take as             fixed the other agents actions.  In simple cases, an assumption of              common knowledge of rationality on the part of the players must be              added.  In more complicated cases, such as when multiple equilibria             are present, common knowledge of rationality and the assumption of              belief-rationality are not enough, since there exists a whole set of            rational beliefs, and no player can ever be certain that the others             believe he has certain beliefs.  In these cases it becomes necessary            to explicitly model the process of belief formation.  The model which           Dr. Bicchieri is developing 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 all players the same           theory of counterfactuals, then it could be shown that the players'             beliefs would eventually converge.  Since there is no way of sorting            out one theory of counterfactuals as the best, or more rational to              adopt, the process of belief formation might never converge, and thus           no equilibrium would be attained.
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{'Code': '135300', 'Text': 'Hist & Philosophy of SET'}
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