Nash Equilibria in Concurrent Games with Lexicographic Preferences

Nash Equilibria in Concurrent Games with Lexicographic Preferences

Julian Gutierrez, Aniello Murano, Giuseppe Perelli, Sasha Rubin, Michael Wooldridge

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 1067-1073. https://doi.org/10.24963/ijcai.2017/148

We study concurrent games with finite-memory strategies where players are given a Buchi and a mean-payoff objective, which are related by a lexicographic order: a player first prefers to satisfy its Buchi objective, and then prefers to minimise costs, which are given by a mean-payoff function. In particular, we show that deciding the existence of a strict Nash equilibrium in such games is decidable, even if players' deviations are implemented as infinite memory strategies.
Keywords:
Knowledge Representation, Reasoning, and Logic: Game Theory
Agent-based and Multi-agent Systems: Agent Theories and Models
Agent-based and Multi-agent Systems: Formal verification, validation and synthesis