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We consider the problem of computing a mixed-strategy generalized Nashequilibrium (MS-GNE) for a class of games where each agent has both continuousand integer decision variables. Specifically, we propose a novel Bregmanforward-reflected-backward splitting and design distributed algorithms thatexploit the problem structure. Technically, we prove convergence to avariational MS-GNE under mere monotonicity and Lipschitz continuityassumptions, which are typical of continuous GNE problems. Finally, we show theperformance of our algorithms via numerical experiments.

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