A sufficient condition for invariance of essential components (Q1913572)

It is shown that a component of the Nash equilibria of a finite game for which the local degree of the projection map from the Nash graph into the space of games has nonzero degree retains this property when a redundant strategy is added; e.g., when a mixed strategy is treated as a pure strategy. A subsequent working paper shows that the local degree is itself invariant to the addition of redundant strategies and coincides with the fixed-point index of the component.