Bargaining games

Abstract

A two-person bargaining game is an ordered pair (F, d), where F is a subset of ℝ² and where d is a point in ℝ². The elements of F are called feasible outcomes (utility pairs), which the players can reach if they cooperate. In case of no cooperation the disagreement outcome d results, with utility d _i for player i ∈ {1, 2}. The problem is on which outcome to agree. Many solutions are proposed and much work has been done in this field (Cf. A. Roth (1979), A. Roth (1985), H. Peters (1992)). The basis was laid by J. Nash (1950). Let Ɓ be the family of bargaining games (F, d) with the following properties:

• (B.1) F is non-empty, convex, closed and comprehensive,¹

• (B.2) {x ∈ F | x ≥ d} is bounded,

• (B.3) there exists an x⁰ ∈ F with x⁰ > d.