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：我们研究在多玩家非零和无限持续时间序贯图博弈中关于理性行为的两个自然问题：检验问题（判断由Mealy机定义的策略轮廓是否理性）与理性验证（判断对给定策略的所有理性回答是否满足特定规范）。针对两大理性概念——纳什均衡和子博弈完美均衡，以及五类主要收益函数——奇偶性、平均收益、定量可达性、能量和折扣和，我们给出了这些问题的复杂度结果。