In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement and the notion of negotiation function. We establish that the set of plays that are supported by SPEs are exactly those that are consistent with the least fixed point of the negotiation function. Finally, we show that the negotiation function is piecewise linear and can be analyzed using the linear algebraic tool box.

翻译：在本文中,我们提供了一种有效的特征描述,描述在有平均回报目标的限定图表上玩的无限长的游戏中所有亚游戏完美平衡。为此,我们引入了要求的概念和谈判功能的概念。我们确定,得到特殊目的设备支持的剧本恰恰是那些与谈判功能中最不固定点相一致的剧本。最后,我们显示,谈判功能是线形线性的,可以使用线性代数工具箱加以分析。