Strategic Behavior and Counterfactuals

在博弈论中，在囚徒困境等博弈情境中定义理性行为的困难在于，参与者的策略将取决于他们对其他参与者策略的预期。这些期望是玩家参与游戏的信念。博弈论认为这些信念在客观上是正确的这种特殊意义上是理性的，但没有解释产生这种信念系统属性的机制。然而，在大多数情况下，这种合理性要求不足以保证达到均衡。在这项研究资助下，Bicchieri博士专注于认知理性假设与均衡之间的关系。所谓均衡，她指的是一种行为的组合，即如果其他行为者的行为是固定的，那么没有一个行为者会想要改变自己的行为。在简单的情况下，必须添加参与者的理性常识假设。在更复杂的情况下，例如存在多重均衡时，理性的常识和信念理性的假设是不够的，因为存在一整套理性信念，没有参与者能够确定其他人相信他有某些信念。在这些情况下，有必要对信念形成过程进行明确的建模。Bicchieri博士正在开发的模型赋予参与者一种反事实理论，他们用它来限制可能的均衡集。如果可以将相同的反事实理论归因于所有参与者，那么可以证明参与者的信念最终会趋同。由于没有办法选出一种反事实理论是最好的，或者是更合理的，信念形成的过程可能永远不会收敛，因此不会达到平衡。

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.