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A condition for determinacy of optimal strategies in zero-sum convex polynomial games

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  • Arias-R., Omar Fdo.

Abstract

The main purpose of this paper is to prove that if there is a non-expansive map relating the sets of optimal strategies for a convex polynomial game, then there exists only one optimal strategy for solving that game. We introduce the remark that those sets are semi-algebraic. This is a natural and important property deduced from the polynomial payments. This property allows us to construct the space of strategies with an infinite number of semi-algebraic curves. We semi-algebraically decompose the set of strategies and relate them with non-expansive maps. By proving the existence of an unique fixed point in these maps, we state that the solution of zero-sum convex polynomial games is determined in the space of strategies.

Suggested Citation

  • Arias-R., Omar Fdo., 2014. "A condition for determinacy of optimal strategies in zero-sum convex polynomial games," MPRA Paper 57099, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:57099
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    References listed on IDEAS

    as
    1. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    2. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    3. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
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    More about this item

    Keywords

    determinacy; polynomial game; semi-algebraic set and function;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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