𝑛-person games with only 1, 𝑛-1, and 𝑛-person coalitions

A considerable amount of work has been done on n-person games in which all coalitions with less than n-1 players are totally defeated. Maschler [3] has studied the structure of their bargaining sets, while Lucas, in two separate papers [1], [2] has given a symmetric solution to such games and studied the behavior of solutions for such games in partition function form. In this paper, we propose to give all discriminatory solutions to such games. We consider here n-person games, v, satisfying