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Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions

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  • Bertrand Crettez

    () (Université Panthéon-Assas, Paris II, CRED, EA 7321)

Abstract

Abstract We compare two notions of equilibrium for other-regarding agents, namely Berge and unilateral support equilibria. A Berge equilibrium is a strategy profile such that the teammates of each agent choose their strategies in order to maximize his utility. A unilateral support equilibrium is a strategy profile such that the teammates of each agent non-cooperatively choose their strategies to maximize his utility. By definition the level of cooperation in a unilateral support equilibrium is no higher than in a Berge equilibrium. Yet, relying on ideas from Team theory, we provide conditions under which a unilateral support equilibrium is also a Berge equilibrium. We also provide conditions under which a unilateral support equilibrium is a Berge–Vaisman equilibrium, i.e., a strategy profile which is a Berge equilibrium and such that the payoff of each player is no lower than his maximin value.

Suggested Citation

  • Bertrand Crettez, 2019. "Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(4), pages 727-739, December.
  • Handle: RePEc:spr:jqecon:v:17:y:2019:i:4:d:10.1007_s40953-019-00168-w
    DOI: 10.1007/s40953-019-00168-w
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    References listed on IDEAS

    as
    1. Bertrand Crettez, 2017. "On Sugden’s “mutually beneficial practice” and Berge equilibrium," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 64(4), pages 357-366, December.
    2. A.M. Colman & T.W. Körner & O. Musy & T. Tazdaït, 2011. "Mutual support in games: Some properties of Berge equilibria," Post-Print hal-00716357, HAL.
    3. Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
    4. Larbani, Moussa & Nessah, Rabia, 2008. "A note on the existence of Berge and Berge-Nash equilibria," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 258-271, March.
    5. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2015. "How To Play Games? Nash Versus Berge Behaviour Rules," Economics and Philosophy, Cambridge University Press, vol. 31(1), pages 123-139, March.
    6. Bertrand Crettez, 2017. "A New Sufficient Condition for a Berge Equilibrium to be a Berge–Vaisman Equilibrium," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 15(3), pages 451-459, September.
    7. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    8. J. Marschak, 1955. "Elements for a Theory of Teams," Management Science, INFORMS, vol. 1(2), pages 127-137, January.
    9. Guala, Francesco & Mittone, Luigi & Ploner, Matteo, 2013. "Group membership, team preferences, and expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 183-190.
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    More about this item

    Keywords

    Berge equilibrium; Berge–Vaisman equilibrium; Berge–Nash equilibrium; Unilateral support equilibrium; Team optimal solution; Person-by-person optimal solution; Mutually beneficial practice;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D - Microeconomics

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