Sequentially compatible payoffs and the core in TU-games

In the context of cooperative TU-games, we introduce a recursive procedure to distribute the surplus of cooperation when there is an exogenous ordering among the set of players N. In each step of the process, using a given notion of reduced games, an upper and a lower bound for the payoff to the player at issue are required. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. For a family of reduction operations, the behavior of this new solution concept is analyzed. For any ordering of N, the core of the game turns out to be the set of sequentially compatible payoffs when the Davis-Maschler reduced games are used. Finally, we study which reduction operations give an advantage to the first player in the ordering.