This paper is a contribution to the problem of sustainable cooperation in an extensive-form game. We study an extension of the subgame-perfect core concept to more broad class of games (when the payoffs are defined at all nodes) which is based on the payoff distribution procedure approach. The properties of this β -S-P Core are studied and algorithm of its implementation in a 2-player game is provided. Using this algorithm we construct specific payoff distribution procedure from the β -S-P Core in an extensive-form version of the fishery-management model with asymmetric players.