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Berge Solution Concepts in the Graph Model for Conflict Resolution

Author

Listed:
  • Giannini Italino Alves Vieira

    (Universidade Federal do Ceará
    Graduate Program in Modelling and Quantitative Methods)

  • Leandro Chaves Rêgo

    (Universidade Federal do Ceará
    Universidade Federal de Pernambuco)

Abstract

In this work, we generalize Berge solution concepts in the graph model for conflict resolution for conflicts with 2 or more decision makers (DMs). These concepts are useful to the analysis of interactions among DMs with altruistic behaviors. Berge behavior can be observed in conflicts where DMs act altruistically expecting others to reciprocate so that in the end it is in their own self-interests to behave in this way. The Berge stabilities presented are inspired on commonly used stability notions in the GMCR, such as: generalized metarationality, symmetric metarationality, sequential and symmetric sequential stabilities for conflicts with 2 or more DMs. We investigate the relation among these proposed concepts and also between such concepts and the standard ones. We also establish a relationship between Berge stability and coalition Nash stability of a modified conflict. The chicken and stag hunt games are used as examples to illustrate applications of the Berge stabilities in conflicts. In particular, we show that in the stag hunt game and in a modified version of it, Berge stabilities may be used to select a more desired Nash equilibria.

Suggested Citation

  • Giannini Italino Alves Vieira & Leandro Chaves Rêgo, 2020. "Berge Solution Concepts in the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 29(1), pages 103-125, February.
    • Handle: RePEc:spr:grdene:v:29:y:2020:i:1:d:10.1007_s10726-019-09650-5
    DOI: 10.1007/s10726-019-09650-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. D. Marc Kilgour & Keith W. Hipel & Liping Fang & Xiaoyong (John) Peng, 2001. "Coalition Analysis in Group Decision Support," Group Decision and Negotiation, Springer, vol. 10(2), pages 159-175, March.
    5. K W Li & D M Kilgour & K W Hipel, 2005. "Status quo analysis in the graph model for conflict resolution," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 699-707, June.
    6. Theodore C. Bergstrom, 1999. "Systems of Benevolent Utility Functions," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 71-100, January.
    7. Fang, Liping & Hipel, Keith W. & Kilgour, D. Marc, 1989. "Conflict models in graph form: Solution concepts and their interrelationships," European Journal of Operational Research, Elsevier, vol. 41(1), pages 86-100, July.
    8. Takehiro Inohara & Keith W. Hipel, 2008. "Coalition analysis in the graph model for conflict resolution," Systems Engineering, John Wiley & Sons, vol. 11(4), pages 343-359, December.
    9. 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.
    10. D. Marc Kilgour & Keith W. Hipel, 2005. "Introduction to the Special Issue on the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 14(6), pages 439-440, November.
    11. D. Marc Kilgour & Keith W. Hipel, 2005. "The Graph Model for Conflict Resolution: Past, Present, and Future," Group Decision and Negotiation, Springer, vol. 14(6), pages 441-460, November.
    12. Haiyan Xu & D. Marc Kilgour & Keith W. Hipel, 2011. "Matrix Representation of Conflict Resolution in Multiple-Decision-Maker Graph Models with Preference Uncertainty," Group Decision and Negotiation, Springer, vol. 20(6), pages 755-779, November.
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