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Uniformity and games decomposition

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Abstract

We introduce the classes of uniform and non-interactive games. We study appropriate projection operators over the space of finite games in order to propose a novel canonical direct-sum decomposition of an arbitrary game into three components, which we refer to as the uniform with zero-constant, the non-interactive total-sum zero and the constant components. We prove orthogonality between the components with respect to a natural extension of the standard inner product and we further provide explicit expressions for the closet uniform and non-interactive games to a given game. The, we characterize the set of its approximate equilibria in terms of the uniformly mixed and dominant strategies equilibria profiles of its closet uniform and non-interactive games respectively

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  • Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini, 2014. "Uniformity and games decomposition," Documents de travail du Centre d'Economie de la Sorbonne 14084r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Mar 2017.
    • Handle: RePEc:mse:cesdoc:14084r
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    References listed on IDEAS

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    1. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
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    More about this item

    Keywords

    Decomposition of games; projection operator; dominant strategy equilibrium; uniformly mixed strategy;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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