Many complete information games have equilibria only in mixed strategies, where players are required to randomize over pure strategies among which they are indifferent according to a fixed probability distribution. Harsanyi showed that, if such a game were perturbed – with each player observing an idiosyncratic independent payoff shock with continuous support – then the perturbed games will have pure strategy equilibria which will converge to the mixed strategy equilibrium as the perturbations become small. We review the strong conditions on perturbations under which Harsanyi’s result holds and discuss weaker conditions on perturbations which ensure the existence of pure strategy equilibria without approximating all mixed equilibria of the unperturbed game.
Approachability Complete information games Correlation Extensive form games Finite dynamic games Harsanyi, J. C. Incomplete information games Mixed strategy equilibria Nash equilibrium Normal form games Overlapping generations model Pure strategy equilibria Purification Regular Nash equilibrium Subgame perfection
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