We study two natural problems about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: checking problems, that consist in deciding whether a strategy profile, defined by a Mealy machine, is rational; and rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of those problems for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for five major classes of payoff functions: parity, mean-payoff, quantitative reachability, energy, and discounted-sum.

翻译：我们研究了图博弈中多人非零和序列无限持续博弈中关于理性行为的两个自然问题：检查问题，即判定由米利机定义的策略配置是否为理性的；以及理性验证，即判定对给定策略的所有理性反应是否满足某些规范。针对两个主要理性概念——纳什均衡与子博弈完美均衡，以及五类主要收益函数——奇偶性、平均收益、定量可达性、能量与折扣和，我们给出了这些问题的计算复杂度。