Index and Robustness of Mixed Equilibria: An Algebraic Approach

Lucas Pahl

Papers from arXiv.org

Abstract: We present two results regarding the relation of the index of equilibria and the index of fixed points, and the index of equilibria and payoff-robustness: any integer can be the index of an isolated completely mixed equilibrium of a finite game. In a particular class of isolated completely mixed equilibria, called monogenic, the index can be 0, +1 or -1 only. In this class non-zero index is equivalent to payoff-robustness. We also discuss extensions of the method of computation to extensive-form games, and cases where the equilibria might be located on the boundary of the strategy set. These results follow from a new method of computing indices of equilibria, which we also develop in this paper, that is based on algebraic properties of the system of polynomials describing completely mixed equilibria.

Date: 2026-03, Revised 2026-10
New Economics Papers: this item is included in nep-gth and nep-mic
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