We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our method employs a version of the double oracle, iteratively adding strategies based on best response to the equilibrium of the empirical MFG among strategies considered so far. We present Fictitious Play (FP) and Replicator Dynamics as two subroutines for computing the empirical game equilibrium. Each subroutine is implemented with a query-based method rather than maintaining an explicit payoff matrix as in typical EGTA methods due to a representation issue we highlight for MFGs. We prove that a Nash equilibrium (NE) exists in the empirical MFG and show the convergence of iterative EGTA to NE of the full MFG with either subroutine. We test the performance of iterative EGTA in various games and show that it outperforms directly applying FP to MFGs in terms of iterations of strategy introduction.
翻译:我们利用实证游戏理论分析框架(EGTA)提出一种模拟方法来解决中度野外游戏(MFGs),我们采用一种模拟方法,利用实证游戏理论分析框架(EGTA)解决中度野外游戏(MFGs),我们采用一种模拟方法,在对迄今考虑的战略之间对实证游戏(MFG)的平衡作出最佳反应的基础上,迭接地添加战略。我们提出Fictious Play(FP)和复制动力作为计算实证游戏平衡的两个子路由。我们用一种基于查询的方法执行每个子路程,而不是像我们为MFGs强调的一个典型的 EGTA方法那样,保持一个明确的回报矩阵。我们证明,在实证MFGs中存在一种纳什平衡(NE),并表明整个MFGs的迭接式 EGTA与NE与任何一种子路由,我们测试反复的EGTA在各种游戏中的表现,并表明它超越了FP在战略引入中直接适用于MFGs。