Value, Consistency, and Random Coalition Formation

Abstract Given an n -player cooperative game and a feasible “age” n -vector suppose that the players in a cooperative game are randomly split into two coalitions, each with a randomly chosen leader; the two leaders bargain bilaterally and each pays, out of his share, a wage to each member of his coalition as specified by the wage vector. The wage vector is said to be consistent with the above procedure if it is equal to the ex ante expected payoff vector. We prove that if all 2-coalition partitions are equally likely and if the bilateral bargain splits the surplus equally then the unique consistent payoff vector is the Shapley value. An equivalent consistency result holds for partitions with more than two elements. These results are related to Gul's (1989) result on noncooperative implementation of the Shapley value. Journal of Economic Literature Classification Number 026.