An asynchronous distributed and scalable generalized Nash equilibrium seeking algorithm for strongly monotone games
Carlo Cenedese, Giuseppe Belgioioso, Sergio Grammatico, Ming Cao
Abstract
In this paper, we present three distributed algorithms to solve a class of Generalized Nash Equilibrium (GNE) seeking problems in strongly monotone games. The first one (SD-GENO) is based on synchronous updates of the agents, while the second and the third (AD-GEED and AD-GENO) represent asynchronous solutions that are robust to communication delays. AD-GENO can be seen as a refinement of AD-GEED, since it only requires node auxiliary variables, enhancing the scalability of the algorithm. Our main contribution is to prove convergence to a v-GNE variational-GNE (vGNE) of the game via an operator-theoretic approach. Finally, we apply the algorithms to network Cournot games and show how different activation sequences and delays affect convergence. We also compare the proposed algorithms to a state-of-the-art algorithm solving a similar problem, and observe that AD-GENO outperforms it.