The competitive bargaining set for cooperative n-person games

Abstract

The continuum of solutions constituting the bargaining set for n-person games in characteristic function form (n ≥ 4) reflects various degrees of determinateness to form a coalition, different requirements of stability, or different levels of competition among the players. At one end of this continuum is the kernel solution. A new solution, called the competitive bargaining set, constitutes the other extreme. It incorporates the concept of a multiobjection, which is based on the idea that threats may be perceived and considered simultaneously even though their simultaneous implementation is impossible. For the simple homogeneous majority games [n − 2, 1, 1, …, 1] the competitive bargaining set (1) yields unique outcomes for each coalition structure, (2) coincides with von Neumann and Morgenstern's main simple solution for certain coalition structures, and (3) converges to Shapley value as n → ∞ when the grand coalition forms. Mathematical and experimental implications of the new solution are discussed briefly.