The Query Complexity of Correlated Equilibria

We consider the complexity of finding a Correlated Equilibrium in an n-player game in a model that allows the algorithm to make queries for players’ utilities at pure strategy profiles. Many randomized regret-matching dynamics are known to yield an approximate correlated equilibrium quickly: in time that is polynomial in the number of players, n, the number of strategies of each player, m, and the approximation error, ǫ−1. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate equilibrium and no efficient randomized algorithm can reach an exact equilibrium.