IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.04661.html
   My bibliography  Save this paper

Pricing with algorithms

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.04661
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yu Awaya & Vijay Krishna, 2016. "On Communication and Collusion," American Economic Review, American Economic Association, vol. 106(2), pages 285-315, February.
    2. James W. Friedman, 1973. "A Non-cooperative Equilibrium for Supergames: A Correction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 435-435.
    3. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    4. Zach Y. Brown & Alexander MacKay, 2023. "Competition in Pricing Algorithms," American Economic Journal: Microeconomics, American Economic Association, vol. 15(2), pages 109-156, May.
    5. Martino Banchio & Andrzej Skrzypacz, 2022. "Artificial Intelligence and Auction Design," Papers 2202.05947, arXiv.org.
    6. Sylvain Chassang & Kei Kawai & Jun Nakabayashi & Juan Ortner, 2022. "Robust Screens for Noncompetitive Bidding in Procurement Auctions," Econometrica, Econometric Society, vol. 90(1), pages 315-346, January.
    7. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Werner, Tobias, 2021. "Algorithmic and human collusion," DICE Discussion Papers 372, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    2. Porter, Robert H., 2020. "Mergers and coordinated effects," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    3. Takashi Kamihigashi & Taiji Furusawa, 2007. "Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 210, Research Institute for Economics & Business Administration, Kobe University.
    4. Odenkirchen, Johannes, 2017. "Pricing Behavior of Cartel Outsiders in Incomplete Cartels," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168309, Verein für Socialpolitik / German Economic Association.
    5. Tracy Xiao Liu & Jenna Bednar & Yan Chen & Scott Page, 2019. "Directional behavioral spillover and cognitive load effects in multiple repeated games," Experimental Economics, Springer;Economic Science Association, vol. 22(3), pages 705-734, September.
    6. Hinloopen, Jeroen & Onderstal, Sander, 2014. "Going once, going twice, reported! Cartel activity and the effectiveness of antitrust policies in experimental auctions," European Economic Review, Elsevier, vol. 70(C), pages 317-336.
    7. Spagnolo, Giancarlo, 2005. "Managerial incentives and collusive behavior," European Economic Review, Elsevier, vol. 49(6), pages 1501-1523, August.
    8. Robert Gagné & Simon van Norden & Bruno Versaevel, 2003. "Testing Optimal Punishment Mechanisms Under Price Regulation: the Case of the Retail Market for Gasoline," CIRANO Working Papers 2003s-57, CIRANO.
    9. Martin, Simon & Rasch, Alexander, 2022. "Collusion by algorithm: The role of unobserved actions," DICE Discussion Papers 382, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    10. Georgios Petropoulos & Thanos Athanasopoulos & Burak Dindaroglu, 2021. "Stability of collusion and quality differentiation- a Nash bargaining approach," Bruegel Working Papers 43226, Bruegel.
    11. Jan Potters & Sigrid Suetens, 2013. "Oligopoly Experiments In The Current Millennium," Journal of Economic Surveys, Wiley Blackwell, vol. 27(3), pages 439-460, July.
    12. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
    13. Marie-Laure Allain & Marcel Boyer & Jean-Pierre Ponssard & Rachidi Kotchoni, 2011. "The Determination of Optimal Fines in Cartel Cases - The Myth of Underdeterrence," CIRANO Working Papers 2011s-34, CIRANO.
    14. Dou, Winston Wei & Ji, Yan & Wu, Wei, 2021. "Competition, profitability, and discount rates," Journal of Financial Economics, Elsevier, vol. 140(2), pages 582-620.
    15. Garrod, Luke, 2012. "Collusive price rigidity under price-matching punishments," International Journal of Industrial Organization, Elsevier, vol. 30(5), pages 471-482.
    16. Hinloopen, Jeroen & Onderstal, Sander & Treuren, Leonard, 2020. "Cartel stability in experimental first-price sealed-bid and English auctions," International Journal of Industrial Organization, Elsevier, vol. 71(C).
    17. Gonzalo Ballestero, 2021. "Collusion and Artificial Intelligence: A computational experiment with sequential pricing algorithms under stochastic costs," Young Researchers Working Papers 1, Universidad de San Andres, Departamento de Economia, revised Oct 2022.
    18. George J. Mailath & Volker Nocke & Lucy White, 2017. "When And How The Punishment Must Fit The Crime," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(2), pages 315-330, May.
    19. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    20. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2013. "Optimal collusion with limited liability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 203-227, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2205.04661. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.