Learning to Collude in a Pricing Duopoly

References

• Abada I, Lambin X (2020) Artificial intelligence: Can seemingly collusive outcomes be avoided? Preprint, submitted April 17, https://dx.doi.org/10.2139/ssrn.3559308.Google Scholar
• Aksoy-Pierson M, Allon G, Federgruen A (2013) Price competition under mixed multinomial logit demand functions. Management Sci. 59(8):1817–1835.Link, Google Scholar
• Assad S, Clark R, Ershov D, Xu L (2020) Algorithmic pricing and competition: Empirical evidence from the German retail gasoline market. CESifo Working paper ISSN 2364–1428.Google Scholar
• Ballard D, Naik A (2017) Algorithms, artificial intelligence, and joint conduct. CPI Antitrust Chronicle, 2:29–35.Google Scholar
• Beneke F, Mackenrodt MO (2020) Remedies for algorithmic tacit collusion. J. Antitrust Enforcement, 9(1):152–176.Crossref, Google Scholar
• Bertomeu J, Evans JH III, Feng M, Tseng A (2013) Tacit collusion and voluntary disclosure: Theory and evidence from the U.S. automotive industry. Management Sci. 67(3):1851–1875.Link, Google Scholar
• Besbes O, Zeevi A (2009) Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Oper. Res. 57(6):1407–1420.Link, Google Scholar
• Besbes O, Zeevi A (2015) On the (surprising) sufficiency of linear models for dynamic pricing with demand learning. Management Sci. 61(4):723–739.Link, Google Scholar
• Broadie M, Cicek D, Zeevi A (2011) General bounds and finite-time improvement for the Kiefer-Wolfowitz stochastic approximation algorithm. Oper. Res. 59(5):1211–1224.Link, Google Scholar
• Brousseau V, Kirman A (1992) Apparent convergence of learning processes in mis-specified games. Dutta B, Mookherjee D, Parthasarathy T, Raghavan TES, Ray D, Tijs S, eds. Game Theory and Economic Applications (Springer-Verlag, Berlin), 303?331.Google Scholar
• Brown Z, MacKay A (2019) Competition in pricing algorithms. Working paper No. w28860, National Bureau of Economic Research.Google Scholar
• Bubeck S, Stoltz G, Yu JY (2011a) Lipschitz bandits without the Lipschitz constant. Kivinen J, Szepesvári C, Ukkonen E, Zeugmann T, eds. Internat. Conf. Algorithmic Learning Theory. ALT 2011. Lecture Notes in Computer Science, vol. 6925 (Springer, Berlin, Heidelberg), 144–158.Google Scholar
• Bubeck S, Munos R, Stoltz G, Szepesvári C (2011b) X-armed bandits. J. Machine Learn. Res. 12:1655–1695.Google Scholar
• Calvano E, Calzolari G, Denicoló V, Pastorello S (2020) Artificial intelligence, algorithmic pricing, and collusion. Amer. Econom. Rev. 110(10):3267–3297.Crossref, Google Scholar
• Capobianco A, Gonzaga P (2017) Algorithms and competition: Friends or foes? Competition Policy International, 1, 2.Google Scholar
• Chen B, Chao X, Wang Y (2020a) Data-based dynamic pricing and inventory control with censored demand and limited price changes. Oper. Res. 68(5):1445–1456.Link, Google Scholar
• Chen Q, Jasin S, Duenyas I (2019) Nonparametric self-adjusting control for joint learning and optimization of multiproduct pricing with finite resource capacity. Math. Oper. Res. 44(2):601–631.Link, Google Scholar
• Chen Q, Jasin S, Duenyas I (2020b) Technical note: Joint learning and optimization for multi-product pricing with finite resource capacity and unknown demand parameters. Oper. Res. 69(2):560–573.Google Scholar
• Cheung WC, Simchi-Levi D, Wang H (2017) Technical note—Dynamic pricing and demand learning with limited price experimentation. Oper. Res. 65(6):1722–1731.Link, Google Scholar
• Cooper WL, Homem-de Mello T, Kleywegt AJ (2015) Learning and pricing with models that do not explicitly incorporate competition. Oper. Res. 63(1):86–103.Link, Google Scholar
• den Boer AV (2014) Dynamic pricing with multiple products and partially specified demand distribution. Math. Oper. Res. 39(3):863–888.Link, Google Scholar
• den Boer AV (2015) Dynamic pricing and learning: Historical origins, current research, and new directions. Surveys Oper. Res. Management Sci. 20(1):1–18.Crossref, Google Scholar
• den Boer AV, Keskin NB (2022) Dynamic pricing with demand learning and reference effects. Management Sci. Forthcoming.Link, Google Scholar
• den Boer AV, Zwart B (2014) Simultaneously learning and optimizing using controlled variance pricing. Management Sci. 60(3):770–783.Link, Google Scholar
• Ezrachi A, Stucke M (2016) Virtual Competition: The Promise and Perils of the Algorithm-Driven Economy (Harvard University Press, Cambridge, MA).Crossref, Google Scholar
• Ezrachi A, Stucke M (2017a) Algorithmic collusion: Problems and counter-measures. Roundtable Algorithms Collusion (OECD). Accessed February 4, 2022, https://one.oecd.org/document/DAF/COMP/WD(2017)25/en/pdf.Google Scholar
• Ezrachi A, Stucke M (2017b) Artificial intelligence & collusion: When computers inhibit competition. Univ. Illinios Law Rev. 1775.Google Scholar
• Ezrachi A, Stucke M (2017c) Two artificial neural networks meet in an online hub and change the future (of competition, market dynamics and society). University of Tennessee Legal Studies Research Paper No. 323.Google Scholar
• Ezrachi A, Stucke ME (2020) Sustainable and unchallenged algorithmic tacit collusion. Northwestern J. Tech. Intellectual Property 17(2):217–260.Google Scholar
• Ferreira KJ, Simchi-Levi D, Wang H (2018) Online network revenue management using Thompson sampling. Oper. Res. 66(6):1586–1602.Link, Google Scholar
• Fox E, Gerard D (2017) EU Competition Law. Cases, Texts and Context (Edward Elgar Publishing, Cheltenham, UK).Google Scholar
• Gal M (2017) Algorithmic-facilitated coordination: Market and legal solutions. CPI Antitrust Chronicle, 22–28. Google Scholar
• Gal MS (2018) Illegal pricing algorithms. Comm. ACM. 62(1):18–20.Crossref, Google Scholar
• Gal MS (2019) Algorithms as illegal agreements. Berkeley Tech. Law J. 34(67):67–118.Google Scholar
• Gata JE (2018) Controlling algorithmic collusion: Short review of the literature, undecidability, and alternative approaches. Preprint, submitted February 15, https://dx.doi.org/10.2139/ssrn.3334889.Google Scholar
• Green E, Marshall R, Marx L (2013) Tacit collusion in oligopoly. Blair R, Sokol D, eds. The Oxford Handbook of International Antitrust Economics, vol. 2 (Oxford University Press, New York), 464–497.Google Scholar
• Hansen K, Misra K, Pai M (2021) Algorithmic collusion: Supra-competitive prices via independent algorithms. Marketing Sci. 40(1):1–12.Google Scholar
• Harrington J Jr (2018) Developing competition law for collusion by autonomous price-setting agents. J. Competition Law Econom. 14(3):331–363.Crossref, Google Scholar
• Harrison JM, Keskin NB, Zeevi A (2012) Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Sci. 58(3):570–586.Link, Google Scholar
• Hoffman B (2018) Competition and consumer protection implications of algorithms, artificial intelligence, and predictive analytics. Remarks at FTC Hearings on Competition and Consumer Protection in the 21st Century, Washington, DC. Accessed February 4, 2022, https://www.ftc.gov/system/files/documents/public_statements/1431041/hoffman_-_ai_intro_speech_11-14-18.pdf.Google Scholar
• Hovenkamp H (2016) Federal Antitrust Policy: The Law of Competition and Its Practice, 5th ed. (West Academic Publishing, St. Paul, MN).Google Scholar
• Hu M, Wang Z, Feng Y (2020) Information disclosure and pricing policies for sales of network goods. Oper. Res. 68(4):1162–1177.Link, Google Scholar
• Ittoo A, Petit N (2017) Algorithmic pricing agents and tacit collusion: A technological perspective. Jacquemin H, De Streel A, eds. L’intelligence Artificielle et le Droit (Larcier, Brussels), 241–256.Crossref, Google Scholar
• Izquierdo S, Izquierdo L (2015) The “win-continue, lose-reverse” rule in Cournot oligopolies: Robustness of collusive outcomes. Amblard F, Miguel F, Blanchet A, Gaudou B, eds. Advances in Artificial Economics, Lecture Notes in Economics and Mathematical Systems, vol. 676 (Springer, Cham), 33–44.Google Scholar
• Jones A, Sufrin B (2016) EU Competition Law: Text, Cases, and Materials, 6th ed. (Oxford University Press, New York).Google Scholar
• Kehl-Waas B (2020) Algorithmic collusion in electronic markets: A simulation with Q-learning agents. Unpublished master’s thesis, University of Turku, Finland.Google Scholar
• Keskin NB, Zeevi A (2014) Dynamic pricing with an unknown demand model: Asymptotically optimal semi-myopic policies. Oper. Res. 62(5):1142–1167.Link, Google Scholar
• Kiefer J, Wolfowitz J (1952) Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23(3):462–466.Crossref, Google Scholar
• Kirman AP (1975) Learning by firms about demand conditions. Day RH, Graves T, eds. Adaptive Economic Models (Academic Press, New York), 137–156.Crossref, Google Scholar
• Kirman AP (1983) Learning in oligopoly: Theory, simulation, and experimental evidence. Frydman R, Phelps ES, eds. Individual Forecasting and Aggregate Outcomes (Cambridge University Press, New York), 147–166.Google Scholar
• Kirman AP (1995) Mistaken beliefs and resultant equilibria. Kirman A, Salmon M, eds. Learning and Rationality in Economics (Blackwell Publishers, Cambridge, MA), 127–178.Google Scholar
• Klein T (2018) Assessing autonomous algorithmic collusion: Q-learning under short-run price commitments. Tinbergen Institute Discussion Paper TI 2018-056/VII, Amsterdam.Google Scholar
• Kleinberg R, Slivkins A, Upfal E (2008) Multi-armed bandits in metric spaces. Proc. 40th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 681–690.Google Scholar
• Kühn KU, Tadelis S (2017) Algorithmic collusion. Presentation prepared for CRESSE, 12th Internat. Conf. Competition and Regulation “Advances in the Analysis of Competition Policy and Regulation”, Heraklion-Crete, https://www.cresse.info/wp-content/uploads/2020/02/2017_sps5_pr2_Algorithmic-Collusion.pdf.Google Scholar
• Loots T, den Boer AV (2021) Data-driven collusion and competition in a pricing duopoly with multinomial logit demand. Preprint, submitted October 6, https://dx.doi.org/10.2139/ssrn.3916076.Google Scholar
• Mehra S (2016) Antitrust and the robo-seller: Competition in the time of algorithms. Minnesota Law Rev. 204(100):1323–1376.Google Scholar
• Nambiar M, Simchi-Levi D, Wang H (2019) Dynamic learning and pricing with model misspecification. Management Sci. 65(11):4980–5000.Link, Google Scholar
• Okuliar A, Kamenir E (2017) Pricing algorithms: Conscious parallelism or conscious commitment? Competition Policy International, 1–4.Google Scholar
• Organisation for Economic Co-operation and Development (2017) Algorithms and collusion: Competition policy in the digital age. Accessed February 4, 2022, www.oecd.org/competition/algorithms-collusion-competition-policy-in-the-digital-age.htm.Google Scholar
• Phillips RL (2005) Pricing and Revenue Optimization (Stanford University Press, Stanford, CA).Crossref, Google Scholar
• Salcedo B (2015) Pricing algorithms and tacit collusion. Working paper, Salcedo institution, Pennsylvania State University.Google Scholar
• Schrepel T (2017) Here’s why algorithms are NOT (really) a thing. Accessed May 2017, Concurrentialiste.Google Scholar
• Schwalbe U (2018) Algorithms, machine learning, and collusion. J. Competition Law Econom. 14(4):568–607.Crossref, Google Scholar
• Smejkal V (2017) Cartels by robots—Current antitrust law in search of an answer. Inter EU Law East: J. Internat. Eur. Law Econom. Market Integrations 4(2):1–18.Google Scholar
• Spall JC (1992) Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automatic Control 37(3):332–341.Crossref, Google Scholar
• Spiridonova A, Juchnevicius E (2020) Price algorithms as a threat to competition under the conditions of digital economy: Approaches to antimonopoly legislation of BRICS countries. BRICS Law J. 7(2):94–117.Crossref, Google Scholar
• Tesauro G, Kephart JO (2002) Pricing in agent economies using multi-agent Q-learning. Autonomic Agents Multi Agent Systems 5(1):289–304.Crossref, Google Scholar
• van de Geer R, den Boer AV (2022) Price optimization under the finite-mixture logit model. Management Sci. Forthcoming.Link, Google Scholar
• Veljanovski C (2020) Algorithmic antitrust. Preprint, submitted August 3, https://dx.doi.org/10.2139/ssrn.3644363.Google Scholar
• Waltman L, Kaymak U (2015) Q-learning agents in a Cournot oligopoly model. J. Econom. Dynamic Control 32:3275–3293.Crossref, Google Scholar
• Wang Y, Chen B, Simchi-Levi D (2021) Multimodal dynamic pricing. Management Sci. 67(10):6136–6152.Google Scholar
• Wang Z, Deng S, Ye Y (2014) Close the gaps: A learning-while-doing algorithm for single-product revenue management problems. Oper. Res. 62(2):318–331.Link, Google Scholar
• Whish R, Bailey D (2018) Competition Law, 9th ed. (Oxford University Press, New York).Crossref, Google Scholar
• Xie K, Mao ZE, Wu J (2019) Learning from peers: The effect of sales history disclosure on peer-to-peer short-term rental purchases. Internat. J. Hospitality Management 76(A):173–183.Crossref, Google Scholar
• Yang Y, Lee YC, Chen PA (2020) Competitive demand learning: A data-driven pricing algorithm. Preprint, submitted August 12, https://arxiv.org/abs/2008.05195.Google Scholar
• Zheng R, Yuan Y, Li Y (2021) Sales disclosure and pricing policies in the presence of social learning. Math. Problems Engrg. 2021:1–16.Crossref, Google Scholar