IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2022i56p12-27.html
   My bibliography  Save this article

Existence theorems for Nash equilibrium and equilibrium in secure strategies

Author

Listed:
  • Iskakov, M.

    (V. A. Trapeznikov Institute of Control Sciences RAS, Moscow)

Abstract

The paper proposes a method for constructing existence theorems for equilibrium in secure strategies (EinSS) on the basis of the well-known existence theorems for Nash equilibrium. The system of definitions of the EinSS is interpreted as the development of the logic of rational behavior in the defi nition of Nash equilibrium. It is proved that under the condition of "strong threats" for the existence of EinSS, it is sufficient to fulfill the conditions of the known existence theorem for the Nash equilibrium only on the sets of secure strategies. This statement is formulated both globally and locally, and is an effective tool for application to practical problems. It opens up the possibility of constructing various particular existence theorems for EinSS. As a demonstration of the proposed approach, from the Debreu's theorem of the existence of social equilibrium, the corresponding theorem of the existence of the EinSS is obtained.

Suggested Citation

  • Iskakov, M., 2022. "Existence theorems for Nash equilibrium and equilibrium in secure strategies," Journal of the New Economic Association, New Economic Association, vol. 56(4), pages 12-27.
    • Handle: RePEc:nea:journl:y:2022:i:56:p:12-27
    DOI: 10.31737/2221-2264-2022-56-4-1
    as

    Download full text from publisher

    File URL: http://www.econorus.org/repec/journl/2022-56-12-27r.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.31737/2221-2264-2022-56-4-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    2. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    3. Iskakov, A. & Iskakov, M., 2017. "In Search of a Generalized Concept of Rationality," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 181-189.
    4. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Documents de travail du Centre d'Economie de la Sorbonne 09061, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
    6. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," PSE-Ecole d'économie de Paris (Postprint) hal-00750953, HAL.
    7. Iskakov, M. & Iskakov, A. & d'Aspremont, C., 2018. "Games for cautious players: The Equilibrium in Secure Strategies," Games and Economic Behavior, Elsevier, vol. 110(C), pages 58-70.
    8. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    9. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    10. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    11. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
    12. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    13. iskakov, Mikhail & ISKAKOV, Alexey, 2012. "Equilibrium in secure strategies," LIDAM Discussion Papers CORE 2012061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00750953, HAL.
    15. Marina S. Sandomirskaia, 2014. "A Model Of Tacit Collusion: Nash-2 Equilibrium Concept," HSE Working papers WP BRP 70/EC/2014, National Research University Higher School of Economics.
    16. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426402, HAL.
    17. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Post-Print halshs-00426402, HAL.
    18. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
    19. Guoqiang Tian, 2009. "The Existence of Equilibria in Games with Arbitrary Strategy Spaces and Payoffs: A Full Characterization," Levine's Working Paper Archive 814577000000000160, David K. Levine.
    20. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    21. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Post-Print hal-00750953, HAL.
    22. Ron Holzman, 2001. "The comparability of the classical and the Mas-Colell bargaining sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 543-553.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iskakov, M. & Iskakov, A. & d'Aspremont, C., 2018. "Games for cautious players: The Equilibrium in Secure Strategies," Games and Economic Behavior, Elsevier, vol. 110(C), pages 58-70.
    2. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    3. He, Wei & Yannelis, Nicholas C., 2015. "Discontinuous games with asymmetric information: An extension of Reny's existence theorem," Games and Economic Behavior, Elsevier, vol. 91(C), pages 26-35.
    4. Carmona, Guilherme & Podczeck, Konrad, 2014. "Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 130-178.
    5. Oriol Carbonell-Nicolau, 2015. "Further results on essential Nash equilibria in normal-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 277-300, June.
    6. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    7. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    8. Guilherme Carmona & Konrad Podczeck, 2016. "Existence of Nash equilibrium in ordinal games with discontinuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 457-478, March.
    9. Zhiwei Liu & Nicholas C. Yannelis, 2013. "On Discontinuous Games with Asymmetric Information," Economics Discussion Paper Series 1318, Economics, The University of Manchester.
    10. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    11. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
    12. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    13. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    14. Alejandro Saporiti, 2014. "Power sharing and electoral equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 705-729, April.
    15. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    16. Pavlo Prokopovych, 2016. "Majorized correspondences and equilibrium existence in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 541-552, March.
    17. Guilherme Carmona, 2016. "Reducible equilibrium properties: comments on recent existence results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 431-455, March.
    18. Pavlo Prokopovych & Nicholas C. Yannelis, 2012. "On Uniform Conditions for the Existence of Mixed Strategy Equilibria," Discussion Papers 48, Kyiv School of Economics.
    19. Pavlo Prokopovych, 2013. "The single deviation property in games with discontinuous payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 383-402, June.
    20. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.

    More about this item

    Keywords

    equilibrium in secure strategies; Nash equilibrium; competitive deviations; noncompetitive deviations; Nash equilibrium existence theorems; rational choice theory;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nea:journl:y:2022:i:56:p:12-27. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.