  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.
