Bargaining : Nash, Consensus, or Compromise?

Two solutions are proposed to Nash (1950)’s bargaining problem: the Consensus and Compromise solutions. They present a gradual divergence away from the Nash solution. In terms of axioms, the Nash solution’s Axiom IIA (Independence of Irrelevant Alternatives) is decomposed into several parts, the controversial ones of which are identified and gradually replaced giving rise to the Consensus and Compromise solutions. The two replacement parts are: 1). if the additional room for cooperation induced by the worsening no-cooperation are, for both players, no better than the solution, the solution shall not change; 2). a solution shall not be the best only for one player i.e. each player should make at least some concession, no matter how small