Subgame-perfect Equilibria in Mean-payoff Games

TL;DR

This paper characterizes all subgame-perfect equilibria in infinite-duration mean-payoff games on finite graphs, introducing new concepts and proving the decidability of the equilibrium existence problem.

Contribution

It introduces the notions of requirement and negotiation function, providing a complete characterization of SPEs and establishing their decidability.

Findings

Supported plays are exactly those consistent with the least fixed point of the negotiation function.

The negotiation function is piecewise linear and analyzable via linear algebra.

Decidability of the SPE constrained existence problem is proven.

Abstract

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 analyzed 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.