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A game-theoretic implication of the Riemann hypothesis

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  • Ewerhart, Christian
Abstract
The Riemann hypothesis (RH) is one of the major unsolved problems in pure mathematics. In the present paper, a parameterized family of non-cooperative games is constructed with the property that, if RH is true, then any game in the family admits a unique Nash equilibrium. We argue that this result is not degenerate. Indeed, neither is the conclusion a tautology, nor is RH used to define the family of games.

Suggested Citation

  • Ewerhart, Christian, 2024. "A game-theoretic implication of the Riemann hypothesis," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 52-59.
    • Handle: RePEc:eee:matsoc:v:128:y:2024:i:c:p:52-59
    DOI: 10.1016/j.mathsocsci.2024.01.007
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    References listed on IDEAS

    as
    1. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    2. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    3. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    4. David K. Levine & Andrea Mattozzi, 2022. "Success in contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 595-624, April.
    5. 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.
    6. Christian Ewerhart, 2021. "A typology of military conflict based on the Hirshleifer contest," ECON - Working Papers 400, Department of Economics - University of Zurich.
    7. 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.
    8. Becker, Johannes Gerd & Damianov, Damian S., 2006. "On the existence of symmetric mixed strategy equilibria," Economics Letters, Elsevier, vol. 90(1), pages 84-87, January.
    9. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    10. Ewerhart, Christian & Sun, Guang-Zhen, 2018. "Equilibrium in the symmetric two-player Hirshleifer contest: Uniqueness and characterization," Economics Letters, Elsevier, vol. 169(C), pages 51-54.
    11. Baik, Kyung Hwan, 1998. "Difference-form contest success functions and effort levels in contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 685-701, November.
    12. Christian Ewerhart & Guang-Zhen Sun, 2018. "Equilibrium in the symmetric Hirshleifer contest: uniqueness and characterization," ECON - Working Papers 286, Department of Economics - University of Zurich.
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