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 straightforward. 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 (Econometrica 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 Décision, pp. 251–263, 1969) $\lambda$—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.