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

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

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
• 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

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