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Pricing with algorithms

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  • Rohit Lamba
  • Sergey Zhuk

Abstract

This paper studies Markov perfect equilibria in a repeated duopoly model where sellers choose algorithms. An algorithm is a mapping from the competitor's price to own price. Once set, algorithms respond quickly. Customers arrive randomly and so do opportunities to revise the algorithm. In the simple game with two possible prices, monopoly outcome is the unique equilibrium for standard functional forms of the profit function. More generally, with multiple prices, exercise of market power is the rule -- in all equilibria, the expected payoff of both sellers is above the competitive outcome, and that of at least one seller is close to or above the monopoly outcome. Sustenance of such collusion seems outside the scope of standard antitrust laws for it does not involve any direct communication.

Suggested Citation

  • Rohit Lamba & Sergey Zhuk, 2022. "Pricing with algorithms," Papers 2205.04661, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2205.04661
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    References listed on IDEAS

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    7. John Asker, 2010. "A Study of the Internal Organization of a Bidding Cartel," American Economic Review, American Economic Association, vol. 100(3), pages 724-762, June.
    8. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    9. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    10. Vikas Kumar, 2012. "Cartels in the Kautiliya Arthasastra," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 6(1), pages 59-79, March.
    11. Joseph E Harrington, 2018. "Developing Competition Law For Collusion By Autonomous Artificial Agents," Journal of Competition Law and Economics, Oxford University Press, vol. 14(3), pages 331-363.
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    Cited by:

    1. Eshwar Ram Arunachaleswaran & Natalie Collina & Sampath Kannan & Aaron Roth & Juba Ziani, 2024. "Algorithmic Collusion Without Threats," Papers 2409.03956, arXiv.org, revised Dec 2024.

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