Bregman algorithms for mixed-strategy generalized Nash equilibrium seeking in a class of mixed-integer games

TL;DR

This paper introduces a novel Bregman splitting method for computing mixed-strategy generalized Nash equilibria in mixed-integer games, providing convergence guarantees and demonstrating effectiveness through numerical experiments.

Contribution

It develops a new Bregman forward-reflected-backward splitting algorithm tailored for mixed-integer GNE problems, with proven convergence under standard assumptions.

Findings

Algorithm converges to a variational MS-GNE under monotonicity and Lipschitz conditions.

Distributed algorithms exploit problem structure for efficiency.

Numerical experiments validate the algorithm's performance.

Abstract

We consider the problem of computing a mixed-strategy generalized Nash equilibrium (MS-GNE) for a class of games where each agent has both continuous and integer decision variables. Specifically, we propose a novel Bregman forward-reflected-backward splitting and design distributed algorithms that exploit the problem structure. Technically, we prove convergence to a variational MS-GNE under mere monotonicity and Lipschitz continuity assumptions, which are typical of continuous GNE problems. Finally, we show the performance of our algorithms via numerical experiments.