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Dynamics and axiomatics of the equal area bargaining solution

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New York : Springer
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  • Mathematics

Abstract

71z;01jan00 Int J Game Theory (2000) 29:81–92 99992000 Dynamics and axiomatics of the equal area bargaining solution* Emilio Calvo1;��, Hans Peters2;��� 1 Departamento de Analisis Economico, Campus dels Tarongers, Avinguda dels Tarongers s/n, Edificio Departamental Oriental, 46011 Valencia, Spain (e-mail: [email protected]) 2 Department of Quantitative Economics, University of Maastricht, 6200 MD Maastricht, The Netherlands (e-mail: [email protected]) Received: November 1998 / Revised version: September 1999 Abstract. We present an alternative formulation of the two-person equal area bargaining solution based on a dynamical process describing the disagreement point set. This alternative formulation provides an interpretation of the idea of equal concessions. Furthermore, it leads to an axiomatic characterization of the solution. Key words: Bargaining, dynamics, equal area solution 1. Introduction One way to compare the axiomatic approaches to the two-person bargaining problem since Nash (1950) can be based on the following question: On which feasible points, beside the disagreement point, should a bargaining solution depend? The Nash bargaining solution depends only on a small neighborhood of the solution point, more precisely, on the slope of the Pareto optimal set at the solution point. Kalai and Smorodinsky (1975) criticized the Nash bar- gaining solution exactly for that reason; they axiomatized a solution proposed earlier by Rai¤a (1953), which depends also on the utopia point. Perles and Maschler (1981) proposed and characterized the so-called Super-Additive so- lution, which depends on the whole Pareto optimal boundary. Another solu- tion which depends on the whole boundary – and thus on the whole feasible * The authors are indebted to two anonymous referees for some valuable comments. ** Emilio Calvo acknowledges support from the MEC under grant No. PB96-0247 and from the Universidad del Pais Vasco-EHU under grant UPV 036.321-HA046/97. *** Stimulating discu

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