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On Berge Equilibria


  • Rabia Nessah

    () (IESEG School of Management (LEM-CNRS))

  • Moussa Larbani

    () (IIUM University Kuala Lumpur)

  • Tarik Tazdait



Based on the notion of equilibrium of a coalition P relatively to a coalition K, of Berge, Zhukovskii has introduced Berge equilibrium as an alternative solution to Nash equilibrium for non cooperative games in normal form. The essential advantage of this equilibrium is that it does not require negotiation of any player with the remaining players, which is not the case when a game has more than one Nashequilibrium. The problem of existence of Berge equilibrium is more difficult (compared to that of Nash). This paper is a contribution to the problem of existence and computation of Berge equilibrium of a non cooperative game. Indeed, using the g-maximum equality, we establish the existence of a Berge equilibrium of a non-cooperative game in normal form. In addition, we give sufficient conditions for theexistence of a Berge equilibrium which is also a Nash equilibrium. This allows us to get equilibria enjoying the properties of both concepts of solution. Finally, using these results, we provide two methods for the computation of Berge equilibria: the first one computes Berge equilibria; the second one computes Berge equilibria which are also Nash equilibria.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Rabia Nessah & Moussa Larbani & Tarik Tazdait, 2009. "On Berge Equilibria," Working Papers 2010-ECO-16, IESEG School of Management.
  • Handle: RePEc:ies:wpaper:e201016

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    References listed on IDEAS

    1. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
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    Cited by:

    1. 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.
    2. repec:wsi:igtrxx:v:13:y:2011:i:03:n:s0219198911003027 is not listed on IDEAS
    3. Messaoud Deghdak & Monique Florenzano, 2011. "On The Existence Of Berge'S Strong Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 325-340.
    4. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
    5. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game," CIRED Working Papers halshs-00271464, HAL.

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