A strategic product for belief functions

• 成果类型: Article
• 署名作者: Stauber, Ronald
• 署名单位: Australian National University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2019.04.004
• 发表日期: 2019
• 页码: 38-64
• 关键词: Belief functions; Product capacities; Equilibrium under ambiguity; strategic uncertainty

摘要

The term belief function is generally used to refer to a class of capacities that can be viewed as representing ambiguity averse preferences. This paper introduces a definition of equilibrium for normal-form games with ambiguous beliefs, where belief functions are used to describe strategic uncertainty. To capture independence of strategies and beliefs, a novel notion of a strategic product integral is introduced for belief functions, based on their Mobius transforms, and shown to be different from the Choquet integral of an appropriate product capacity. A characterization of the integral in terms of maxmin expected utility expressed relative to elements of the cores of the respective belief functions, is also presented. The resulting equilibrium notion relies on Mobius transforms to embed objectively chosen probabilistic mixed strategies into ambiguous beliefs of opponents about these strategies, while incorporating stronger consistency requirements than those imposed by previous definitions of equilibria under ambiguity. (C) 2019 Elsevier Inc. All rights reserved.