Are Equilibrium Strategies Unaffected by Incentives?

Abstract

In a mixed-strategy Nash equilibrium, changing one player's payoffs affects only the other player's equilibrium strategy mix. This `Payoff Irrelevance Proposition' (PIP) appears to undercut the main foundations of economic policy analysis since, allegedly, equilibrium behavior will not respond to changes in incentives. We show, in contrast, that: (1) When the policy-maker has the first move in a sequential-move game, the PIP does not hold. (2) Even in a simultaneous-move game, the PIP holds only when the policy space is discrete, and for sufficiently small payoff revisions. Thus, incentives do generally affect behavior in equilibrium.