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 a recent breakthrough, Babichenko and Rubinstein REF proved the first lower bound on the communication complexity of finding an approximate Nash equilibrium.
Communication complexity of approximate Nash equilibria
STOC 2017
Computer Science Mathematics