AriasR., Omar Fdo. (2014): A condition for determinacy of optimal strategies in zerosum convex polynomial games.

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Abstract
The main purpose of this paper is to prove that if there is a nonexpansive 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 semialgebraic. 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 semialgebraic curves. We semialgebraically decompose the set of strategies and relate them with nonexpansive maps. By proving the existence of an unique fixed point in these maps, we state that the solution of zerosum convex polynomial games is determined in the space of strategies.
Item Type:  MPRA Paper 

Original Title:  A condition for determinacy of optimal strategies in zerosum convex polynomial games 
English Title:  A condition for determinacy of optimal strategies in zerosum convex polynomial games 
Language:  English 
Keywords:  determinacy, polynomial game, semialgebraic 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,SpringerVerlag, Berlin. 2) Blume, L. and Zame, W. (1994). The algebraic geometry of perfect and sequential equilibrium. Econometrica 62, No. 4, pp. 783794. 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. Reprint of the 1959 original. 5) Kubler, F. and Schmedders, K. (2010). Competitive equilibria in semialgebraic economies. Journal of economic theory 145, 301330. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/57099 