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On the existence of Nash equilibrium in discontinuous games

Author

Listed:
  • Rabia Nessah

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Guoqiang Tian

Abstract

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of very weak continuity, called quasi-weak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. We present applications to show that our conditions allow for economically meaningful payoff discontinuities.

Suggested Citation

  • Rabia Nessah & Guoqiang Tian, 2015. "On the existence of Nash equilibrium in discontinuous games," Post-Print hal-01533554, HAL.
    • Handle: RePEc:hal:journl:hal-01533554
    DOI: 10.1007/s00199-015-0921-8
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    Cited by:

    1. Achille Basile & Vincenzo Scalzo, 2020. "Non-emptiness of the alpha-core: sufficient and necessary conditions," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1143-1153, December.
    2. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    3. Scalzo, Vincenzo, 2023. "Existence and stability results on the unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 1-9.
    4. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    5. Ghislain Herman Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2024. "Justice, inclusion, and incentives," Journal of Theoretical Politics, , vol. 36(2), pages 101-131, April.
    6. Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.
    7. Hanjoon Michael Jung, 2020. "Perfect regular equilibrium," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(4), pages 380-398, December.
    8. Philip J. Reny, 2016. "Introduction to the symposium on discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 423-429, March.
    9. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    10. Oriol Carbonell-Nicolau & Richard P. McLean, 2019. "Nash and Bayes–Nash equilibria in strategic-form games with intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 935-965, November.
    11. Ghislain H. Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Papers 2107.12870, arXiv.org.
    12. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2025. "Nash Equilibrium in Discontinuous Games: A Weakening of Reny’s Robust Better-Reply Correspondence Property," Post-Print hal-05305754, HAL.
    13. Khan, M. Ali & McLean, Richard P. & Uyanik, Metin, 2024. "On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    14. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    15. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    16. Wei He & Nicholas C. Yannelis, 2017. "A remark on discontinuous games with asymmetric information and ambiguity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 119-126, April.
    17. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    18. Vincenzo Scalzo, 2020. "On the uniqueness of Nash equilibrium in discontinuous ordinal and normal form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 163-168, April.
    19. Demeze-Jouatsa, Ghislain-Herman & Pongou, Roland & Tondji, Jean-Baptiste, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Center for Mathematical Economics Working Papers 653, Center for Mathematical Economics, Bielefeld University.
    20. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

    More about this item

    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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