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A strategic product for belief functions

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  • Stauber, Ronald
Abstract
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 Möbius 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 Möbius 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.

Suggested Citation

  • Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
    • Handle: RePEc:eee:gamebe:v:116:y:2019:i:c:p:38-64
    DOI: 10.1016/j.geb.2019.04.004
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    Cited by:

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    2. Frédéric Koessler & Marieke Pahlke, 2023. "Feedback Design in Strategic-Form Games with Ambiguity Averse Players," Working Papers halshs-04039083, HAL.

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    More about this item

    Keywords

    Belief functions; Product capacities; Equilibrium under ambiguity; Strategic uncertainty;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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