English

Rational verification and checking for Nash and subgame-perfect equilibria in graph games

Computer Science and Game Theory 2023-07-17 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2301.12913,
  title  = {Rational verification and checking for Nash and subgame-perfect equilibria in graph games},
  author = {Léonard Brice and Jean-François Raskin and Marie van den Bogaard},
  journal= {arXiv preprint arXiv:2301.12913},
  year   = {2023}
}
R2 v1 2026-06-28T08:26:44.433Z