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Kalai-Smorodinsky Bargaining Solution Equilibria

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Abstract

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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  • Giuseppe De Marco & Jacqueline Morgan, 2009. "Kalai-Smorodinsky Bargaining Solution Equilibria," CSEF Working Papers 235, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    • Handle: RePEc:sef:csefwp:235
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    1. Peter Borm & Freek van Megen & Stef Tijs, 1999. "A perfectness concept for multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 401-412, July.
    2. 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.
    3. 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).
    4. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. John Roemer, 2005. "Games with vector-valued payoffs and their application to competition between organizations," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-13.
    8. 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.
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