Equilibrium convergence in large games
证明了大型博弈的纳什均衡对应具有闭图性质,即有限玩家博弈的纳什均衡序列的极限可由大型博弈的纳什均衡诱导,并应用于均衡选择。
This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of finite-player games, the limit of any convergent sequence of Nash equilibria of the corresponding finite-player games can be induced by a Nash equilibrium of the large game. Such a result goes beyond earlier results on the closed graph property for pure strategy Nash equilibrium correspondence in large games in multiple aspects. An application on equilibrium selection in large games is also presented.