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 plays that are supported by SPEs are exactly those that are consistent with a fixed point of the negotiation function. Finally, we use that characterization to prove that the SPE threshold problem, who status was left open in the literature, is decidable.

翻译：本文针对有限图上具有平均收益目标的无限时域博弈，给出了所有子博弈完美均衡的有效刻画。为此，我们引入了"需求"概念与"协商函数"概念。我们证明，存在子博弈完美均衡支撑的博弈进程恰好是与协商函数的不动点相一致的那些进程。最后，我们利用这一刻画证明了子博弈完美均衡阈值问题的可判定性，该问题的状态在文献中此前一直悬而未决。