In this talk, we recall the notion of SPE for games of infinite duration played on graph. We introduce new algorithmic ideas in this context. In particular, 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 set of 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.