Index and Robustness of Mixed Equilibria: An Algebraic Approach

Lucas Pahl

Papers from arXiv.org

Abstract: We present a new method for computation of the index of completely mixed equilibria in finite games, based on the work of Eisenbud et al.(1977). We apply this method to solving two questions about 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.

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