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.

翻译：基于Eisenbud等人（1977）的研究，我们提出了一种计算有限博弈中完全混合均衡指数的新方法。我们将此方法应用于解决两个问题：均衡指数与不动点指数的关系，以及均衡指数与支付鲁棒性的关系。结果表明：任何整数均可作为有限博弈中孤立完全混合均衡的指数。在一类特殊的孤立完全混合均衡（称为单基因均衡）中，指数仅可能为$0$、$+1$或$-1$。在此类均衡中，非零指数等价于支付鲁棒性。我们还讨论了将该计算方法扩展至扩展式博弈的情形，以及均衡可能位于策略集边界的情况。