Arias-R., Omar Fdo.
(2014):
*A condition for determinacy of optimal strategies in zero-sum convex polynomial games.*

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## 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.

Item Type: | MPRA Paper |
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Original Title: | A condition for determinacy of optimal strategies in zero-sum convex polynomial games |

English Title: | A condition for determinacy of optimal strategies in zero-sum convex polynomial games |

Language: | English |

Keywords: | determinacy, polynomial game, semi-algebraic set and function |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games |

Item ID: | 57099 |

Depositing User: | Omar F. Arias |

Date Deposited: | 04 Jul 2014 14:55 |

Last Modified: | 16 Oct 2019 04:50 |

References: | 1) Blume, L. and Zame, W. (1992). The algebraic geometry of competitive equilibrium. Economic theory and international trade; essays in memoriam J. Trout Rader, ed. por W. Neuefeind y R. Reizman,Springer-Verlag, Berlin. 2) Blume, L. and Zame, W. (1994). The algebraic geometry of perfect and sequential equilibrium. Econometrica 62, No. 4, pp. 783-794. 3) Bolte, J., Gaubert, S. and Vigeral, G. (2013). Definable zero sum stochastic games. arXiv:1301.1967v2. 4) Karlin, S. (1992). Mathematical methods and theory in games, programming, and economics. Dover Publications Inc., New York. Vol. I: Matrix games, programming, and mathematical economics; Vol. II: The theory of infinite games. Re-print of the 1959 original. 5) Kubler, F. and Schmedders, K. (2010). Competitive equilibria in semi-algebraic economies. Journal of economic theory 145, 301-330. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/57099 |