Subjective expected utility in games

• 成果类型: Article
• 署名作者: Di Tillio, Alfredo
• 署名单位: Bocconi University; Bocconi University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• 发表日期: 2008-09-01
• 页码: 287-323
• 关键词: Subjective probability; preference hierarchies; type spaces; beliefs hierarchies; common belief; expected utility; incomplete information; correlated equilibria

摘要

This paper extends Savage's subjective approach to probability and utility from decision problems under exogenous uncertainty to choice in strategic environments. Interactive uncertainty is modeled both explicitly, using hierarchies of preference relations, the analogue of beliefs hierarchies, and implicitly, using preference structures, the analogue of type spaces a la Harsanyi, and it is shown that the two approaches are equivalent. Preference structures can be seen as those sets of hierarchies arising when certain restrictions on preferences, along with the players' common certainty of the restrictions, are imposed. Preferences are a priori assumed to satisfy only very mild properties (reflexivity, transitivity, and monotone continuity). Thus, the results provide a framework for the analysis of behavior in games under essentially any axiomatic structure. An explicit characterization is given for Savage's axioms, and it is shown that a hierarchy of relatively simple preference relations uniquely identifies the decision maker's utilities and beliefs of all orders. Connections with the literature on beliefs hierarchies and correlated equilibria are discussed.