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A bargaining model for finite n-person multi-criteria games

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Abstract

In this paper we consider a multi-criteria game model which allows interactions between players. The problem addressed is considered as a cooperative game in order to achieve consensus solutions which are evaluated with respect to several criteria simultaneously. The main idea consists of analyzing finite multi-criteria n-person games as multi-criteria bargaining games. The notion of Pareto-optimal guaranteed payoffs as a generalization of the maximin values of scalar games is proposed, together with two different solution concepts which can be characterized as the solutions of multi-criteria linear programming problems. A procedure to incorporate additional information about the agents' preferences in order to reach a final consensus is also provided.

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  • Luisa Monroy & Amparo M. Mármol & Victoriana Rubiales, 2005. "A bargaining model for finite n-person multi-criteria games," Economic Working Papers at Centro de Estudios Andaluces E2005/21, Centro de Estudios Andaluces.
    • Handle: RePEc:cea:doctra:e2005_21
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    1. Paolo Cubiotti, 2000. "Existence Of Generalised Pareto Equilibria For Constrained Multiobjective Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 329-344.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Borm, Peter & Vermeulen, Dries & Voorneveld, Mark, 2003. "The structure of the set of equilibria for two person multicriteria games," European Journal of Operational Research, Elsevier, vol. 148(3), pages 480-493, August.
    4. M. Voorneveld, 1999. "Pareto-Optimal Security Strategies as Minimax Strategies of a Standard Matrix Game," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 203-210, July.
    5. Zhao, Jingang, 1991. "The Equilibria of a Multiple Object Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 171-182.
    6. E. Allevi & A. Gnudi & I.V. Konnov & S. Schaible, 2003. "Noncooperative Games with Vector Payoffs Under Relative Pseudomonotonicity," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 245-254, August.
    7. S. X. Li, 1998. "Cone Concavity and Multiple-Payoff Constrained n-Person Games," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 119-149, April.
    8. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    Finite multi-criteria games. Bargaining games. Multi-criteria analysis;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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