A Consensus-based Stochastic Nash Equilibrium Algorithm

With the rise of generative adversarial nets,the algorithms for solving Nash equi-librium of game dynamics have become a research hotspot.A series of good algorithms have been proposed successively.However,these algorithms are all gradient-based methods,which will lead to local solutions inevitably in the games with multiple Nash equilibria.We propose a consensus-based stochastic Nash Equilibrium algorithm in-spired by the idea of consensus-based optimization method.It can find the global op-timal Nash equilibrium in the high-dimensional multiplayer game with multiple Nash equilibria.In this dissertation,dynamic weights are designed based on Boltzmann dis-tribution to enhance the stability of the algorithm,which is well behaved in numerical results.At the same time,the mean-field limits and Laplace principle are used to verify its rationality.We further provide convergence results under the time-discrete algo-rithm.The convergence condition and the error analysis of the algorithm are given under certain conditions.Numerical experiments show the effectiveness of the algo-rithm.