2023/01/30 by Brice, Léonard, Raskin, Jean-François, Bogaard, Marie van den
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2301.12913
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.