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.
翻译:我们考虑的是计算一种混合战略通用纳什平衡(MS-GNE)的问题,这种混合战略是每一种游戏,其中每个代理都具有连续和整数决定变量。具体地说,我们提出一个新的布雷格曼前向反向反向分裂法,并设计利用问题结构的分布式算法。技术上,我们证明在单调和利普西茨连续性假设下,我们与可变的MS-GNE趋同,这在GNE的持续问题中是典型的。最后,我们通过数字实验展示了我们算法的性能。