  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.

Computer Science and Game Theory