Sample Complexity of Solving Non-Cooperative Games

Abstract

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner, in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with ∈ accuracy. First, we consider the class G of all N-player non-cooperative games with a continuous action space that admit at least one NE. Using information-theoretic inequalities, a lower bound on the complexity of solving G is derived which depends on the Kolmogorov 2∈-capacity of the constraint set and the total capacity of the com..