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A game-theoretic implication of the Riemann hypothesis

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  • Christian Ewerhart

Abstract

The Riemann Hypothesis (RH) is one of the major unsolved problems in pure mathematics. In this note, a parameterized family of non-cooperative games is constructed with the property that, if RH holds true, then any game in this 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 defi ne the family of games.

Suggested Citation

  • Christian Ewerhart, 2022. "A game-theoretic implication of the Riemann hypothesis," ECON - Working Papers 410, Department of Economics - University of Zurich, revised May 2023.
    • Handle: RePEc:zur:econwp:410
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    4. 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.
    5. 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.
    6. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    7. 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.
    8. Christian Ewerhart, 2021. "A typology of military conflict based on the Hirshleifer contest," ECON - Working Papers 400, Department of Economics - University of Zurich.
    9. 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.
    10. 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.
    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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    Keywords

    Riemann hypothesis; Nash equilibrium;

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