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Delegate Pricing to Algorithms: When Slow and Steady Wins the Race

Author

Listed:
  • Galit Ashkenazi-Golan
  • Edward Plumb
  • Clemens Possnig
  • Yufei Zhang

Abstract

We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, each firm strictly prefers faster learning. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a dominant action in the stage game and convergence to this price is guaranteed, we prove that firms design sluggish algorithms in equilibrium.

Suggested Citation

  • Galit Ashkenazi-Golan & Edward Plumb & Clemens Possnig & Yufei Zhang, 2026. "Delegate Pricing to Algorithms: When Slow and Steady Wins the Race," Papers 2610.11675, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2610.11675
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    References listed on IDEAS

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    1. Emilio Calvano & Giacomo Calzolari & Vincenzo Denicolò & Sergio Pastorello, 2020. "Artificial Intelligence, Algorithmic Pricing, and Collusion," American Economic Review, American Economic Association, vol. 110(10), pages 3267-3297, October.
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    3. Zach Y. Brown & Alexander MacKay, 2023. "Competition in Pricing Algorithms," American Economic Journal: Microeconomics, American Economic Association, vol. 15(2), pages 109-156, May.
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    5. Stephanie Assad & Robert Clark & Daniel Ershov & Lei Xu, 2024. "Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market," Journal of Political Economy, University of Chicago Press, vol. 132(3), pages 723-771.
    6. Chaim Fershtman & Kenneth L. Judd, 2006. "Equilibrium Incentives in Oligopoly: Corrigendum," American Economic Review, American Economic Association, vol. 96(4), pages 1367-1367, September.
    7. Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-366, May.
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