Mixed Nash Equilibria in Concurrent Terminal-Reward Games

Patricia Bouyer (1) , Nicolas Markey (1) , Daniel Stan (1)

1 LSV - Laboratoire Spécification et Vérification [Cachan]

We study mixed-strategy Nash equilibria in multiplayer deterministic concurrent games played on graphs, with terminal-reward payoffs (that is, absorbing states with a value for each player). We show undecidability of the existence of a constrained Nash equilibrium (the constraint re-quiring that one player should have maximal payoff), with only three players and 0/1-rewards (i.e., reachability objectives). This has to be compared with the undecidability result by Um-mels and Wojtczak for turn-based games which requires 14 players and general rewards. Our proof has various interesting consequences: (i) the undecidability of the existence of a Nash equilibrium with a constraint on the social welfare; (ii) the undecidability of the existence of an (unconstrained) Nash equilibrium in concurrent games with terminal-reward payoffs.

Domaines: Informatique et théorie des jeux [cs.GT]

Patricia Bouyer, Nicolas Markey, Daniel Stan. Mixed Nash Equilibria in Concurrent Terminal-Reward Games. FSTTCS 2014, Dec 2014, Delhi, India. ⟨10.4230/LIPIcs.FSTTCS.2014.351⟩. ⟨hal-01105081⟩