论文标题
分析有限状态的Ergodic Master方程
Analysis of the Finite-State Ergodic Master Equation
论文作者
论文摘要
平均野外游戏模型在具有连续玩家的游戏中模拟平衡，以限制对称$ n $玩家游戏的系统，玩家之间的互动较弱。我们考虑有两个成本标准的有限状态，无限的水平问题：折扣和雄性。在Lasry-Lions单调条件下，我们通过两个耦合方程的平均场游戏系统来表征固定的Ergodic平均野外游戏平衡：一个用于值，另一个用于固定度量。该系统与Ergodic Master方程相关联。使用几种打折的平均现场游戏系统来设置相关的折扣主方程。我们表明，折扣主方程是平稳的，在折扣系数中均匀。将折现因子降至零，我们达到了厄贡主方程的平滑度。
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria: discounted and ergodic. Under the Lasry--Lions monotonicity condition we characterize the stationary ergodic mean field game equilibrium by a mean field game system of two coupled equations: one for the value and the other for the stationary measure. This system is linked with the ergodic master equation. Several discounted mean field game systems are utilized in order to set up the relevant discounted master equations. We show that the discounted master equations are smooth, uniformly in the discount factor. Taking the discount factor to zero, we achieve the smoothness of the ergodic master equation.
