Independent mistakes in large games (Q1423658)

Let \(G\) be an \(n\)-player game in normal form. A noisy equilibrium is a Nash equilibrium of perturbed \(G\), where it is common knowledge that players tremble according to known probability distributions. This paper considers the limits of noisy equilibria as n grows large. The main result is as follows. For continuous payoff functions, for large \(n\), a Nash equilibrium of \(G\) is close to a noisy equilibrium, provided the limit point of Nash equilibrium is generic. The result does not hold for discontinuous payoff functions. Two important counterexamples, bargaining games, and free-rider games, are given.