一句话：引入需求与协商函数，刻画平均支付博弈的所有子博弈完美均衡，并证明SPE阈值问题可判定。
本文研究有限图上无限时长的平均支付博弈。作者给出了这类博弈中所有子博弈完美均衡（SPE）的有效刻画。为此引入“需求”（requirement）与“协商函数”（negotiation function）两个概念，证明由 SPE 支持的游戏轨迹恰好是与协商函数某个不动点一致的轨迹。基于该刻画，作者进一步证明文献中遗留的 SPE 阈值问题是可判定的。该工作为平均支付博弈的均衡分析提供了统一框架，并解决了可判定性开放问题。
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.
@article{paperbot2188,
title = {Subgame-perfect Equilibria in Mean-payoff Games (journal version)},
author = {Léonard Brice and Marie van den Bogaard and Jean-François Raskin},
journal = {Logical Methods in Computer Science},
volume = {Volume 19, Issue 4},
year = {2023},
doi = {10.46298/lmcs-19(4:6)2023}
}