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On the Existence of Pareto Efficient Nash Equilibria in Discontinuous Games

Author

Listed:
  • Rabia Nessah

    (IESEG School of Management, UMR 9221-LEM, F-59000 Lille, France)

  • Raluca Parvulescu

    (IESEG School of Management, UMR 9221-LEM, F-59000 Lille, France)

Abstract

This paper gives existence theorems of pure, Pareto efficient, Nash equilibrium in compact, convex and discontinuous games. These conditions are simple and straightforward to verify. Moreover, the present existence results neither imply nor are implied by the known results in the literature. The results are illustrated by several examples.

Suggested Citation

  • Rabia Nessah & Raluca Parvulescu, 2017. "On the Existence of Pareto Efficient Nash Equilibria in Discontinuous Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-13, September.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500141
    DOI: 10.1142/S0219198917500141
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    References listed on IDEAS

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    1. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    2. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    3. Tarik Tazdaït & Moussa Larbani & Rabia Nessah, 2007. "On Berge Equilibrium," CIRED Working Papers halshs-00271452, HAL.
    4. Scalzo, Vincenzo, 2010. "Pareto efficient Nash equilibria in discontinuous games," Economics Letters, Elsevier, vol. 107(3), pages 364-365, June.
    5. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
    6. Scalzo, Vincenzo, 2012. "Discontinuous stable games and efficient Nash equilibria," Economics Letters, Elsevier, vol. 115(3), pages 387-389.
    7. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    8. Q. H. Ansari & Y. C. Lin & J. C. Yao, 2000. "General KKM Theorem with Applications to Minimax and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 17-57, January.
    9. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
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