Allocation processes in cooperative games

In this paper we attempt to introduce dynamics into the theory of cooperative games. A solution of the game is reached through an allocation process. At each stage of the allocation process of a cooperative game a budget of fixed size is distributed among the players. In the first part of this note we study a type of process that, at any stage, endows the budget to a player whose contribution to the total welfare, according to some measurements, is maximal. It is shown that the empirical distribution of the budget induced by each process of the family converges to a least square value of the game, one such value being the Shapley value. The two other allocation processes converge to the core or the least core. ∗ I am grateful to the Associate Editor and to the two anonymous referees of International Journal of Game Theory