Subgame-perfect Equilibria in Mean-payoff Games (journal version)

TL;DR

This paper characterizes all subgame-perfect equilibria in infinite-duration mean-payoff games on finite graphs, introduces new concepts like requirement and negotiation function, and proves the decidability of the SPE threshold problem.

Contribution

It provides an effective characterization of SPEs using fixed points of the negotiation function and resolves the open question of the decidability of the SPE threshold problem.

Findings

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

The SPE threshold problem is decidable.

Introduces the notions of requirement and negotiation function for mean-payoff games.

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 a fixed point of the negotiation function. Finally, we use that characterization to prove that the SPE threshold problem, who status was left open in the literature, is decidable.