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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 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. Under a natural inner product, we show that the components are orthogonal and we provide explicit expressions for the closet uniform and non interactive games to a given game. We characterize the set of its approximate equilibria in terms of the uniformly mixed and dominant strategies equilibria profiles of its closest uniform and non interactive games respectively

Suggested Citation

  • Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini, 2014. "Uniformity and games decomposition," Documents de travail du Centre d'Economie de la Sorbonne 14084, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:14084
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    1. Norman L. Kleinberg & Jeffrey H. Weiss, 1986. "The Orthogonal Decomposition of Games and an Averaging Formula for the Shapley Value," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 117-124, February.
    2. Sandholm, William H., 2010. "Decompositions and potentials for normal form games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 446-456, November.
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    5. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    6. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
    7. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    8. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    9. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
    10. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, 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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