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A Refinement Concept For Equilibria In Multicriteria Games Via Stable Scalarizations

Author

Listed:
  • GIUSEPPE DE MARCO

    (Dipartimento di Statistica e Matematica, per la Ricerca Economica, Università di Napoli "Parthenope", via Medina 40, 80133 Napoli, Italy)

  • JACQUELINE MORGAN

    (Dipartimento di Matematica e Statistica, Università di Napoli Federico II via Cinthia, 80126, Napoli, Italy)

Abstract

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, calledscalarization-stableequilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:02:n:s0219198907001345
    DOI: 10.1142/S0219198907001345
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    Citations

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    Cited by:

    1. Andreas H. Hamel & Andreas Löhne, 2018. "A set optimization approach to zero-sum matrix games with multi-dimensional payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 369-397, December.
    2. 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.
    3. Yasuo Sasaki, 2019. "Rationalizability in multicriteria games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 673-685, June.
    4. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    5. Zachary Feinstein & Birgit Rudloff, 2021. "Characterizing and Computing the Set of Nash Equilibria via Vector Optimization," Papers 2109.14932, arXiv.org, revised Dec 2022.
    6. Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
    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. Kokkala, Juho & Poropudas, Jirka & Virtanen, Kai, 2015. "Rationalizable Strategies in Games With Incomplete Preferences," MPRA Paper 68331, University Library of Munich, Germany.
    9. Jaeok Park, 2019. "Decision Making and Games with Vector Outcomes," Working papers 2019rwp-146, Yonsei University, Yonsei Economics Research Institute.
    10. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.

    More about this item

    Keywords

    Multicriteria game; Pareto Nash equilibrium; refinement; perturbation; scalarization-stable equilibrium;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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