Subjective Expected Utility in Games
将Savage的主观方法从外生不确定性下的决策问题扩展到策略环境，通过偏好层级构建状态空间，刻画决策者如何形成对其他参与者偏好和信念的信念，并给出Savage公理下的特征化。
This paper extends the scope of Savage’s subjective approach from decision problems under exogenous uncertainty to choice in strategic environments. In these environments the decision maker understands the uncertainty she is facing is affected by other decision makers in a similar situation. This contrast with classical decision making complicates the appropriate specification of the state space: as it is not exogenous, the uncertainty concerns not only the other decision makers ’ choices but also the behavioral rationale behind them. First, this problem is solved, constructing the state space explicitly — using hierarchies of preference relations — and then showing that this space indeed contains every relevant aspect of the decision maker’s uncertainty. Since no restriction on preferences is imposed a priori, these results enable the analysis of behavior in games under any axiomatic structure. Second, conditions on preferences are characterized which imply that the decision maker behaves as if she is sure each other agent has preferences satisfying certain axioms, is himself sure each other agent’s preferences satisfy certain axioms, and so on. Third, such characterization is provided for Savage’s axioms. It is shown that a sequence of preference relations uniquely identifies the decision maker’s utilities and beliefs, and also tells whether according to these beliefs each other agent is an expected utility maximizer, believes each other agent is, and so on.