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Kalai-Smorodinsky Bargaining Solution Equilibria

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Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the rel- ative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered in Roemer (2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations such as the the extension to multicriteria games of the Selten's (1975) trembling hand perfect equilibrium concept.

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Paper provided by Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy in its series CSEF Working Papers with number 235.

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Date of creation: 30 Jul 2009
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Publication status: published in Journal of Optimization, Theory and Applications, 2010, Vol. 145, 429­449
Handle: RePEc:sef:csefwp:235

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  1. Loridan, P. & Morgan, J. & Raucci, R., 1997. "Convergence of Minimal and Approximate Minimal Elements of Sets in Partially Ordered Vector Spaces," Papiers d'Economie Mathématique et Applications 97.94, Université Panthéon-Sorbonne (Paris 1).
  2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  3. Megen, F. van & Borm, P.E.M. & Tijs, S.H., 1995. "A perfectness concept for multicriteria games," Discussion Paper 1995-28, Tilburg University, Center for Economic Research.
  4. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
  5. Giuseppe De Marco & Jacqueline Morgan, 2007. "A Refinement Concept For Equilibria In Multicriteria Games Via Stable Scalarizations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 169-181.
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