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Continuous-Time Best-Response and Related Dynamics in Tullock Contests with Convex Costs

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  • Edith Elkind
  • Abheek Ghosh
  • Paul W. Goldberg

Abstract

Tullock contests model real-life scenarios that range from competition among proof-of-work blockchain miners to rent-seeking and lobbying activities. We show that continuous-time best-response dynamics in Tullock contests with convex costs converges to the unique equilibrium using Lyapunov-style arguments. We then use this result to provide an algorithm for computing an approximate equilibrium. We also establish convergence of related discrete-time dynamics, e.g., when the agents best-respond to the empirical average action of other agents. These results indicate that the equilibrium is a reliable predictor of the agents' behavior in these games.

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  • Edith Elkind & Abheek Ghosh & Paul W. Goldberg, 2024. "Continuous-Time Best-Response and Related Dynamics in Tullock Contests with Convex Costs," Papers 2402.08541, arXiv.org.
    • Handle: RePEc:arx:papers:2402.08541
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Thorlund-Petersen, Lars, 1990. "Iterative computation of cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 2(1), pages 61-75, March.
    3. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    4. Christian Ewerhart & Federico Quartieri, 2020. "Unique equilibrium in contests with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 243-271, July.
    5. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    6. Renaud Bourlès & Yann Bramoullé & Eduardo Perez‐Richet, 2017. "Altruism in Networks," Econometrica, Econometric Society, vol. 85, pages 675-689, March.
    7. Ewerhart, Christian, 2017. "The lottery contest is a best-response potential game," Economics Letters, Elsevier, vol. 155(C), pages 168-171.
    8. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    9. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    10. MOULIN, Hervé & VIAL, Jean-Philippe, 1978. "Strategically zero-sum games: the class of games whose completely mixed equilibria connot be improved upon," LIDAM Reprints CORE 359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    12. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    13. DESCHAMPS, Robert, 1975. "An algorithm of game theory applied to the duopoly problem," LIDAM Reprints CORE 213, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    15. Jacob D. Leshno & Philipp Strack, 2020. "Bitcoin: An Axiomatic Approach and an Impossibility Theorem," American Economic Review: Insights, American Economic Association, vol. 2(3), pages 269-286, September.
    16. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-898, December.
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