For a constant ϵ, we prove a poly(N ) lower bound on the (randomized) communication complexity of ϵ-Nash equilibrium in two-player N × N games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of (ϵ, ϵ)-weak approximate Nash equilibrium, which is a pro le of mixed actions such that at least (1 − ϵ)-fraction of the players are ϵ-best replying. • Theory of computation → Communication complexity; Exact and approximate computation of equilibria; Convergence and learning in games; Communication complexity, approximate Nash equilibria, convergence rate, uncoupled dynamics ACM Reference format:
In REF , in addition to the lower bound for two-player game which we improved, there is also an exponential lower bound for n-player games.
Communication complexity of approximate Nash equilibria
STOC 2017
Computer Science Mathematics