A Characterization of the Nash Bargaining Solution

We characterize the Nash bargaining solution replacing the axiom of Independence of Irrelevant Alternatives with three independent axioms: Independence of Non-Individually Rational Alternatives, Twisting and Disagreement Point Convexity. We give a non-cooperative bargaining interpretation to this last axiom.bargaining problem; Nash solution; axiomatic characterization; Independence of Non-Individually Rational Alternatives; Twisting; Disagreement Point Convexity

BARGAINING IN COMMITTEES OF REPRESENTATIVES: THE OPTIMAL VOTING RULE

Committees are often made up of representatives of different-sized groups of individuals, and make decisions by means of a voting rule which specifies what vote configurations can pass a decision. This raises the question of the choice of the optimal voting rule, given the different sizes of the groups that members represent. In this paper we take a new departure to address this problem, assuming that the committee is a bargaining scenario in which negotiations take place 'in the shadow of the voting rule' in search of unanimous consensus. That is, a general agreement is looked for, but any winning coalition can enforce an agreement.Voting rule, Bargaining, Nash solution.

An axiomatization of the Kalai-Smorodinsky solution when the feasible sets can be finite

選択肢の数が有限であるような交渉問題を含んだ定義域上へKalai-Smorodinsky解(Kalai and Smorodinsky (1975))を拡張した対応(多価関数)の解を定義し、その公理化をおこなう。 つまりその解が上記の定義域上において連続性、独立性、対称性、不変性、単調性を満たす唯一の解である事を証明する。独立性は、効用空間でのHausdorffの距離ではかつてのものである。独立性は、解が対応である事にあわせて拡張したことを除くと、Nashの定義より弱く、Roth(1977)のそれ同じである。対称性、不変性はKalai and Smorodinskyのそれと本質的に変わらない。単調性は、解が対応であるためにKalai and Smorodinskyのそれとは大きく異なった定義となっている。 しかしこの定義を一価関数の解に適用した場合、この公理はオリジナルの単調性に近い性質を持ったものになる

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Maximal symmetry and the Nash solution

The Nash Bargaining Solution is characterised by using the new axiom of Maximal Symmetry in place of Nash's Independence of Irrelevant Alternatives and Symmetry. This axiom expresses the idea that a fair arbitrator should treat symmetric alternatives in the same way, subject to the feasibility constraint. An advantage of the proposed characterisations is that they are valid on a wide set of domains, in particular domains including, or consisting of, non-convex problems.</p

Maximal symmetry and the Nash solution

The Nash Bargaining Solution is characterised by using the new axiom of Maximal Symmetry in place of Nash's Independence of Irrelevant Alternatives and Symmetry. This axiom expresses the idea that a fair arbitrator should treat symmetric alternatives in the same way, subject to the feasibility constraint. An advantage of the proposed characterisations is that they are valid on a wide set of domains, in particular domains including, or consisting of, non-convex problems.</p