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

Abstract

In this paper, we provide an effective characterization of all the subgameperfect 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.This paper is an enhanced version of [BRvdB21]. All the proofs are now included in the main body of the paper, and some of them have been rewrote to be more readable, especially those of Theorems 7.3 and 8.3. The proof of Theorem 4.4 has been modified in order to relax its hypotheses, via a change in the definition of steady negotiation (Definition 3.5). We have also taken advantage of the new available space to add examples in the main body of this paper, especially Example 5.2.