Review of Industrial Organization

, Volume 55, Issue 1, pp 155–171 | Cite as

Algorithmic Pricing What Implications for Competition Policy?

  • Emilio Calvano
  • Giacomo CalzolariEmail author
  • Vincenzo Denicolò
  • Sergio Pastorello


Pricing decisions are increasingly in the “hands” of artificial algorithms. Scholars and competition authorities have voiced concerns that those algorithms are capable of sustaining collusive outcomes more effectively than can human decision makers. If this is so, then our traditional policy tools for fighting collusion may have to be reconsidered. We discuss these issues by critically surveying the relevant law, economics, and computer science literature.


Algorithmic pricing Competition policy Artificial intelligence Machine learning Collusion 

JEL Classification

D42 D82 L42 



We thank the editor Larry White, the guest editors Christos Genakos, Michael Pollitt, and the discussant Patrick Legros and participants at the conference “Celebrating 25 Years of the EU Single Market” organized by the Review of Industrial Organization in Cambridge Judge Business School, 2018. Financial support from the Digital Chair of the Toulouse school of economics is gratefully acknowledged.


  1. Bloembergen, D., Tuyls, K., Hennes, D., & Kaisers, M. (2015). Evolutionary dynamics of multi-agent learning: A survey. Journal of Artificial Intelligence Research, 53, 659–697.CrossRefGoogle Scholar
  2. Busoniu, L., Babuska, R., & De Schutter, B. (2008). A comprehensive survey of multiagent reinforcement learning. IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 38(2), 156–172.CrossRefGoogle Scholar
  3. Calvano, E., Calzolari, G., Denicolò, V., & Pastorello, S. (2018). Artificial intelligence, algorithmic pricing and collusion. CEPR Discussion Paper13405.Google Scholar
  4. Chen, L., Mislove, A., & Wilson, C. (2016). An empirical analysis of algorithmic pricing on Amazon marketplace. In Proceedings of the 25th international conference on world wide web. International World Wide Web Conferences Steering Committee.Google Scholar
  5. Cooper, R. W., DeJong, D. V., Forsythe, R., & Ross, T. W. (1990). Selection criteria in coordination games: Some experimental results. The American Economic Review, 80(1), 218–233.Google Scholar
  6. Cooper, D. J., & Kühn, K. U. (2014). Communication, renegotiation, and the scope for collusion. American Economic Journal: Microeconomics, 6(2), 247–278.Google Scholar
  7. Crandall, J. W., Oudah, M., Tennom, Ishowo-Oloko, F., Abdallah, S., Bonnefon, J., et al. (2018). Cooperating with machines. Nature Communications, 9(233), 2018.Google Scholar
  8. Dogan, I., & Guner, A. R. (2015). A reinforcement learning approach to competitive ordering and pricing problem. Expert Systems, 32, 39–47.CrossRefGoogle Scholar
  9. Doraszelski, U., & Pakes, A. (2007). A framework for applied dynamic analysis in IO. In M. Armstrong & R. H. Porter (Eds.), Handbook of industrial organization (Vol. 3, Chapter 4). Amsterdam: Elsevier Science.Google Scholar
  10. Ellison, G., & Ellison, S. F. (2018). Match quality, search, and the Internet market for used books (No. w24197). National Bureau of Economic Research.Google Scholar
  11. Erev, I., & Roth, A. E. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review, 88, 848–881.Google Scholar
  12. Ezrachi, A., & Stucke, M. E. (2015). Artificial intelligence and collusion: When computers inhibit competition. Oxford Legal Studies Research Paper No. 18/2015, University of Tennessee Legal Studies Research Paper No. 267.Google Scholar
  13. Fudenberg, D., & Levine, D. K. (2016). Whither game theory? Towards a theory of learning in games. The Journal of Economic Perspectives, 30(4), 151–169.CrossRefGoogle Scholar
  14. Harrington, J. E. (2017). Developing competition law for collusion by autonomous agents. Working paper, The Wharton School, University of Pennsylvania.Google Scholar
  15. Hu, J., & Wellman, M. P. (2003). Nash Q-learning for general-sum stochastic games. Journal of machine learning research, 4, 1039–1069.Google Scholar
  16. Lerer, A., & Peysakhovich, A. (2018). Maintaining cooperation in complex social dilemmas using deep reinforcement learning. arXiv preprint arXiv:1707.01068.
  17. Mehra, S. K. (2016). Antitrust and the robo-seller: Competition in the time of algorithms. Minnesota Law Review, 100, 1323–75.Google Scholar
  18. Milgrom, P. R., & Roberts, D. J. (1990). Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica, 58, 1255–1277.CrossRefGoogle Scholar
  19. Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., et al. (2015). Human-level control through deep reinforcement learning. Nature, 518(7540), 529–533. (PMID: 25719670).CrossRefGoogle Scholar
  20. Roth, A. E., & Erev, I. (1995). Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term. Games and Economic Behavior, 8, 164–212.CrossRefGoogle Scholar
  21. Salcedo, B. (2015). Pricing algorithms and tacit collusion. Working paper Pennsylvania State University.Google Scholar
  22. Sannikov, Y., & Skrzypacz, A. (2007). Impossibility of collusion under imperfect monitoring with flexible production. American Economic Review, 97, 1794–1823.CrossRefGoogle Scholar
  23. Sarin, R., & Vahid, F. (2001). Predicting how people play games: A simple dynamic model of choice. Games and Economic Behavior, 34, 104–122.CrossRefGoogle Scholar
  24. Sukhbaatar, S., Szlam, A., & Fergus, R. (2016). Learning multiagent communication with backpropagation. arXiv, preprint arXiv:1605.07736.
  25. Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning: An introduction. Cambridge: MIT press.Google Scholar
  26. Tampuu, A., Matiisen, T., Kodelja, D., Kuzovkin, I., Korjus, K., Aru, J., et al. (2017). Multiagent cooperation and competition with deep reinforcement learning. PLoS ONE, 12(4), e0172395.CrossRefGoogle Scholar
  27. Tesauro, G., & Kephart, J. O. (2002). Pricing in agent economics using multi-agent Q-learning. Autonomous Agents and Multi-Agent Systems, 5, 289–304.CrossRefGoogle Scholar
  28. United States v. David Topkins. (2015). Plea agreement.
  29. Waltman, L., & Kaymak, U. (2008). Q-learning agents in a Cournot oligopoly model. Journal of Economic Dynamics and Control, 32(10), 3275–3293.CrossRefGoogle Scholar
  30. Watkins, C. J. C. H., & Dayan, P. (1992). Q-learning. Machine Learning, 8(279), 292.Google Scholar
  31. Xie, M., & Chen, J. (2004). Studies on horizontal competition among homogeneous retailers through agent-based simulations. Journal of Systems Science and Systems Engineering, 13, 490–505.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze EconomicheUniversity of BolognaBolognaItaly
  2. 2.CEPRLondonUK
  3. 3.Toulouse School of EconomicsToulouseFrance
  4. 4.European University Institute and University of BolognaFlorenceItaly

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