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A perfectness concept for multicriteria games

Author

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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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Yasuo Sasaki, 2019. "Rationalizability in multicriteria games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 673-685, June.
    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. Lucia Pusillo, 2017. "Vector Games with Potential Function," Games, MDPI, vol. 8(4), pages 1-11, September.
    7. 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.
    8. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    9. 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.
    10. 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.

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