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Unilateral Support Equilibria

Author

Listed:
  • Schouten, Jop

    (Tilburg University, Center For Economic Research)

  • Borm, Peter

    (Tilburg University, Center For Economic Research)

  • Hendrickx, Ruud

    (Tilburg University, Center For Economic Research)

Abstract

The concept of Berge equilibria is based on supportive behavior among the players: each player is supported by the group of all other players. In this paper, we extend this concept by maintaining the idea of supportive behavior among the players, but eliminating the underlying coordination issues. We suggest to consider individual support rather than group support. The main idea is to introduce support relations, modeled by derangements. In a derangement, every player supports exactly one other player and every player is supported by exactly one other player. Subsequently, we dene a new equilibrium concept, called a unilateral support equilibrium, which is unilaterally supportive with respect to every possible derangement. We show that a unilateral support equilibrium can be characterized in terms of pay-offfunctions so that every player is supported by every other player individually. Moreover, it is shown that every Berge equilibrium is also a unilateral support equilibrium and we provide an example in which there is no Berge equilibrium, while the set of unilateral support equilibria is non-empty. Finally, the relation between the set of unilateral support equilibria and the set of Nash equilibria is explored.

Suggested Citation

  • Schouten, Jop & Borm, Peter & Hendrickx, Ruud, 2018. "Unilateral Support Equilibria," Discussion Paper 2018-011, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:02dd1da8-0dad-48f8-8fe1-63ae3532d291
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/24538904/2018_011.pdf
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    References listed on IDEAS

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    1. R. Nessah & M. Larbani & T. Tazdait, 2007. "A note on Berge equilibrium," Post-Print hal-00204224, HAL.
    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. 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.
    5. 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.
    6. 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.
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    More about this item

    Keywords

    mutual support equilibria; Berge equilibria; unilateral support equilibria;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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