Subgame-perfect Equilibria in Mean-payoff Games (journal version)
Léonard Brice, Marie van den Bogaard, Jean-François Raskin
TL;DR
The paper addresses the problem of characterizing subgame-perfect equilibria in infinite-duration mean-payoff games on finite graphs. It introduces a fixed-point framework with a negotiation function that updates per-vertex rationality thresholds, proving SPE outcomes are exactly the plays that are consistent with the least fixed point $\lambda^*$ of this function. By connecting to abstract and concrete negotiation games, the authors provide an effective algorithmic path to compute $\lambda^*$ and decide the SPE/ε-SPE threshold problems, with a detailed analysis showing the negotiation function is piecewise affine and computable in double-exponential time. They establish that mean-payoff SPEs always admit a fixed-point representation under steady negotiation and derive tight complexity bounds (NP-hard lower bound; 2-ExpTime upper bound). The results significantly advance synthesis and game-theoretic analysis in quantitative, multi-agent settings by providing a constructive, decidable framework for SPEs beyond finite payoff ranges.
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.