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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.

Suggested Citation

  • 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, revised Oct 2024.
    • Handle: RePEc:arx:papers:2402.08541
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    References listed on IDEAS

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