Axiomatization of the discrete Raiffa solution

Abstract

This article provides an axiomatic characterization of the discrete Raiffa solution for two-person bargaining games. The extension to n > 2 players is straight- forward. This solution had been introduced as one of four "arbitration schemes" by Raiffa (Arbitration schemes for generalized-two person games, 1951; Ann Math Stud 28:361-387, 1953). The axiomatization expresses a consistency property by which the standard midpoint solution for TU-bargaining games can be extended to general NTU-bargaining games. The underlying linear approximation from inside captures a dual view to the linear approximation from outside that underlies Nash's (Economet- rica 18:155-162, 1950) axiomatization of his Nash solution that is also embodied in Shapley's (Utility comparison and the theory of games. In La Decision, pp. 251-263, 1969) λ—transfer principle and, even earlier, in a lemma by Harsanyi (Contributions to the theory of games IV, pp 325-355, 1959). Finally, the present axiomatization is compared with other ones in the literature that are motivated by Kalai (Econometrica 45:1623-1630, 1977) axiom of step-by-step negotiation.