Core Concepts
Efficiently compute Nash equilibrium in time-varying directed graphs using distributed algorithms.
Abstract
The article proposes a distributed algorithm for finding Nash equilibrium in non-cooperative games played over time-varying directed communication networks. It focuses on partial information scenarios, where agents have limited access to others' actions. The algorithm utilizes local information exchange among players and relies on row-stochastic mixing matrices. The analysis shows geometric convergence to the Nash equilibrium under strong convexity and Lipschitz continuity assumptions. Various existing methods and their limitations are discussed, highlighting the efficacy of the proposed approach.
Stats
Each agent performs a gradient step to minimize its own cost function while sharing and retrieving information from neighboring agents.
Numerical simulations for a Nash-Cournot game illustrate the efficacy of the proposed algorithm.
Convergence properties do not depend on augmented mapping but rely on contractivity properties of doubly stochastic matrices.