Subgame-perfect Equilibria in Mean-payoff Games [article]

Léonard Brice, Jean-François Raskin, Marie Van Den Bogaard
2022 arXiv   pre-print
In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with the least fixed point of the negotiation function. Finally, we show that the negotiation function is piecewise linear, and can be
more » ... zed using the linear algebraic tool box. As a corollary, we prove the decidability of the SPE constrained existence problem, whose status was left open in the literature.
arXiv:2101.10685v3 fatcat:j2ofjvjs4vc3vfcehmfyc57cia