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

Omar Fdo. Arias-R.

MPRA Paper from University Library of Munich, Germany

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.

Keywords: determinacy; polynomial game; semi-algebraic set and function (search for similar items in EconPapers)
JEL-codes: C63 C73 (search for similar items in EconPapers)
Date: 2014-07-03
New Economics Papers: this item is included in nep-gth
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