Strategic Behavior and Counterfactuals

在博弈论中，在像囚徒困境这样的博弈情景中定义理性行为的困难在于，玩家的策略将取决于他们对其他玩家策略的期望。这些期望是球员们来到比赛时所怀有的信念。博弈论者假设这些信念在非常特殊的意义上是理性的，即客观上是正确的，但没有对产生信念系统这一属性的机制提供任何解释。然而，在大多数情况下，这样的合理性要求不足以保证将达到平衡。在这项研究拨款下，比奇耶里博士专注于认知理性假设与均衡之间的关系。她所说的均衡是指一系列行动的组合，如果他采取固定的其他代理行动，任何代理人都不会想要改变他的行动。在简单的情况下，必须增加玩家对理性的共同知识的假设。在更复杂的情况下，例如当存在多个均衡时，对理性的常识和信念-理性的假设是不够的，因为存在一整套理性信念，任何参与者都不能确定其他人相信他有特定的信念。在这种情况下，有必要对信念形成的过程进行明确的建模。Bicchieri博士正在开发的模型将反事实理论归因于参与者，他们使用该理论来限制可能的均衡集。如果有可能将同样的反事实理论归因于所有参与者，那么就可以证明，参与者的信念最终会收敛。由于没有办法将一种反事实理论归类为最好的或更合理的采用，信仰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.