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A perfectness concept for multicriteria games

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  • Peter Borm
  • Freek van Megen
  • Stef Tijs

Abstract

This paper considers a refinement of equilibria for multicriteria games based on the perfectness concept of Selten (1975). Existence of perfect equilibrium points is shown and several characterizations are provided. Furthermore, contrary to the result for equilibria for multicriteria games, an example shows that there is no exact correspondence between perfect equilibrium points and the perfect Nash equilibria of the related trade-off games. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:3:p:401-412
    DOI: 10.1007/s001860050057
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    References listed on IDEAS

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    1. Borm, P.E.M. & Tijs, S.H. & van den Aarssen, J.C.M., 1988. "Pareto equilibria in multiobjective games," Other publications TiSEM a02573c0-8c7e-409d-bc75-0, Tilburg University, School of Economics and Management.
    2. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    3. L. S. Shapley & Fred D. Rigby, 1959. "Equilibrium points in games with vector payoffs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 6(1), pages 57-61, March.
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    Cited by:

    1. M. Quant & P. Borm & G. Fiestras-Janeiro & F. Megen, 2009. "On Properness and Protectiveness in Two-Person Multicriteria Games," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 499-512, March.
    2. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    3. L. Petrosjan & J. Puerto, 2002. "Folk theorems in multicriteria repeated N-person games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 275-287, December.
    4. Naouel Yousfi-Halimi & Mohammed Said Radjef & Hachem Slimani, 2018. "Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations," Annals of Operations Research, Springer, vol. 267(1), pages 607-628, August.
    5. Raul P. Lejano & Helen Ingram, 2012. "Modeling the commons as a game with vector payoffs," Journal of Theoretical Politics, , vol. 24(1), pages 66-89, January.
    6. G. De Marco & J. Morgan, 2010. "Kalai-Smorodinsky Bargaining Solution Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 429-449, June.
    7. Giuseppe De Marco & Jacqueline Morgan, 2009. "On Multicriteria Games with Uncountable Sets of Equilibria," CSEF Working Papers 242, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    8. Lucia Pusillo, 2017. "Vector Games with Potential Function," Games, MDPI, vol. 8(4), pages 1-11, September.
    9. Yasuo Sasaki, 2019. "Rationalizability in multicriteria games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 673-685, June.
    10. H. Yu & H. M. Liu, 2013. "Robust Multiple Objective Game Theory," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 272-280, October.

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