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.
Highlights
We focus on a subset of generalized Nash equilibrium (GNE), the so called variational GNE (v-GNE), that has attained growing interest in the recent years– see [6, 8, 21]
To ensure that this change of variables does not affect the equilibrium of the game, we introduce the following result proving that an equilibrium point of the new set of equations is a v-GNE of (2)
Solving a GNE seeking problem in strongly monotone games is possible via AD-GENO in an asynchronous fashion, with node variables only, and by ensuring resilience to delayed information
Summary
Multi-agent network systems arise in several areas, leading to increasing research activities. In [3, 7, 8], the authors focused on developing synchronous and distributed equilibrium seeking algorithms for noncooperative games, namely, the case in which all the agents update their strategies at the same time. To achieve a fully decentralized update rule, we rely only on node auxiliary variables, preserving the scalability in the case of a large number of agents This result is a significant contribution, due to the technical challenges in the asynchronous implementation of the algorithm, addressed by carefully analyzing the influence of the delayed information on the dynamics of the auxiliary variables. A preliminary and partial version of these results were presented in [17]
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