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On the existence of unilateral support equilibrium

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  • Crettez, Bertrand
  • Nessah, Rabia

Abstract

We provide existence and characterization results for unilateral support equilibrium in n-player games. A unilateral support equilibrium is a strategy profile such that the teammates of each agent unilaterally choose their strategies to maximize his payoff. We also consider the case of unilateral support equilibrium relative to a coalition structure, wherein mutual (but still unilateral) support is coalitionaly dependent, and agents who do not belong to a coalition follow a Nash behavior. Further, we compare unilateral support equilibrium with Berge equilibrium, strong Berge equilibrium, strong Nash equilibrium and the α-core. We also compare unilateral support equilibrium relative to a coalition structure with the ℭ-absolute optimal solution.

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  • Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    • Handle: RePEc:eee:matsoc:v:105:y:2020:i:c:p:41-47
    DOI: 10.1016/j.mathsocsci.2020.04.004
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    References listed on IDEAS

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    1. 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.
    2. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2017. "Existence and computation of Berge equilibrium and of two refinements," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 7-15.
    3. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    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. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
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    7. 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.
    8. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
    9. Jingang Zhao, 1999. "The existence of TU -core in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 25-34.
    10. Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
    11. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 422-430.
    12. Rabia Nessah & Moussa Larbani, 2014. "Berge–Zhukovskii Equilibria: Existence And Characterization," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-11.
    13. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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