Journal of Revenue and Pricing Management

, Volume 18, Issue 3, pp 185–203 | Cite as

Dynamic pricing and learning with competition: insights from the dynamic pricing challenge at the 2017 INFORMS RM & pricing conference

  • Ruben van de GeerEmail author
  • Arnoud V. den Boer
  • Christopher Bayliss
  • Christine S. M. Currie
  • Andria Ellina
  • Malte Esders
  • Alwin Haensel
  • Xiao Lei
  • Kyle D. S. Maclean
  • Antonio Martinez-Sykora
  • Asbjørn Nilsen Riseth
  • Fredrik Ødegaard
  • Simos Zachariades
Practice Article


This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29–30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition.


Dynamic pricing Learning Competition Numerical performance 



Chris Bayliss and Christine Currie were funded by the EPSRC under Grant Number EP/N006461/1. Andria Ellina and Simos Zachariades were part funded by EPSRC as part of their PhD studentships. Asbjørn Nilsen Riseth was partially funded by EPSRC Grant EP/L015803/1.


  1. Aghion, P., M.P. Espinosa, and B. Jullien. 1993. Dynamic duopoly with learning through market experimentation. Economic Theory 3 (3): 517–539.Google Scholar
  2. Akcay, Y., H.P. Natarajan, and S.H. Xu. 2010. Joint dynamic pricing of multiple perishable products under consumer choice. Management Science 56 (8): 1345–1361.Google Scholar
  3. Alepuz, M.D., and A. Urbano. 1999. Duopoly experimentation: Cournot competition. Mathematical Social Sciences 37 (2): 165–188.Google Scholar
  4. Anufriev, M., D. Kopányi, and J. Tuinstra. 2013. Learning cycles in Bertrand competition with differentiated commodities and competing learning rules. Journal of Economic Dynamics and Control 37 (12): 2562–2581.Google Scholar
  5. Araman, V., and R. Caldentey. 2009. Dynamic pricing for nonperishable products with demand learning. Operations Research 57 (5): 1169–1188.Google Scholar
  6. Belleflamme, P., and F. Bloch. 2001. Price and quantity experimentation: A synthesis. International Journal of Industrial Organization 19 (10): 1563–1582.Google Scholar
  7. Bergemann, D., and J. Valimaki. 1996. Market experimentation and pricing, Cowles Foundation Discussion Paper 1122, Cowles Foundation for Research in Economics at Yale University, Accessed 5 June 2018.
  8. Bertsimas, D., and G. Perakis. 2006. Dynamic pricing: A learning approach. In Mathematical and Computational Models for Congestion Charging, 45–79. New York: Springer.Google Scholar
  9. Besbes, O., and A. Zeevi. 2009. Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Operations Research 57 (6): 1407–1420.Google Scholar
  10. Bischi, G.I., C. Chiarella, and M. Kopel. 2004. The long run outcomes and global dynamics of a duopoly game with misspecified demand functions. International Game Theory Review 06 (03): 343–379.Google Scholar
  11. Bischi, G.I., A.K. Naimzada, and L. Sbragia. 2007. Oligopoly games with local monopolistic approximation. Journal of Economic Behavior & Organization 62 (3): 371–388.Google Scholar
  12. Boissier, M., R. Schlosser, N. Podlesny, S. Serth, M. Bornstein, J. Latt, J. Lindemann, J. Selke, and M. Uflacker. 2017. Data-driven repricing strategies in competitive markets: An interactive simulation platform. In Proceedings of the Eleventh ACM Conference on Recommender Systems, RecSys’17, 355–357.Google Scholar
  13. Broder, J., and P. Rusmevichientong. 2012. Dynamic pricing under a general parametric choice model. Operations Research 60 (4): 965–980.Google Scholar
  14. Brousseau, V., and A. Kirman. 1992. Apparent convergence of learning processes in mis-specified games. In Game Theory and Economic Applications, ed. B. Dutta, D. Mookherjee, T. Parthasarathy, T.E.S. Raghavan, D. Ray, and S. Tijs, 303–331. Berlin: Springer.Google Scholar
  15. Chen, Y., and V. Farias. 2013. Simple policies for dynamic pricing with imperfect forecasts. Operations Research 61 (3): 612–624.Google Scholar
  16. Cheung, W. C., D. Simchi-Levi, and H. Wang. 2013. Dynamic pricing and demand learning with limited price experimentation, Working paper, Accessed 2 February 2018.
  17. Chung, B.D., J. Li, T. Yao, C. Kwon, and T.L. Friesz. 2012. Demand learning and dynamic pricing under competition in a state-space framework. IEEE Transactions on Engineering Management 59 (2): 240–249.Google Scholar
  18. Cooper, W. L., T.H. de Mello, and A.J. Kleywegt. 2014. Learning and pricing with models that do not explicitly incorporate competition, Working paper, University of Minnesota.
  19. Cyert, R.M., and M.H. DeGroot. 1970. Bayesian analysis and duopoly theory. Journal of Political Economy 78 (5): 1168–1184.Google Scholar
  20. Dasgupta, P., and R. Das. 2000. Dynamic pricing with limited competitor information in a multi-agent economy. In Cooperative information systems. Lecture notes in computer science, vol. 1901, eds. P. Scheuermann, and O. Etzion, 299–310. Berlin, Heidelberg: Springer.Google Scholar
  21. den Boer, A.V. 2015. Dynamic pricing and learning: Historical origins, current research, and new directions. Surveys in Operations Research and Management Science 20 (1): 1–18.Google Scholar
  22. den Boer, A., and B. Zwart. 2014. Simultaneously learning and optimizing using controlled variance pricing. Management Science 60 (3): 770–783.Google Scholar
  23. den Boer, A., and B. Zwart. 2015. Dynamic pricing and learning with finite inventories. Operations Research 63 (4): 965–978.Google Scholar
  24. DiMicco, J.M., P. Maes, and A. Greenwald. 2003. Learning curve: A simulation-based approach to dynamic pricing. Electronic Commerce Research 3 (3–4): 245–276.Google Scholar
  25. Dimitrova, M., and E.E. Schlee. 2003. Monopoly, competition and information acquisition. International Journal of Industrial Organization 21 (10): 1623–1642.Google Scholar
  26. Farias, V., and B. van Roy. 2010. Dynamic pricing with a prior on market response. Operations Research 58 (1): 16–29.Google Scholar
  27. Fisher, M., S. Gallino, and J. Li. 2017. Competition-based dynamic pricing in online retailing: A methodology validated with field experiments. Management Science 64 (6): 2496–2514.Google Scholar
  28. Fishman, A., and N. Gandal. 1994. Experimentation and learning with networks effects. Economics Letters 44 (1–2): 103–108.Google Scholar
  29. Friesz, T. L., C. Kwon, T.I. Kim, L. Fan, and T. Yao. 2012. Competitive robust dynamic pricing in continuous time with fixed inventories. arXiv:1208.4374 [math.OC].
  30. Gallego, A.G. 1998. Oligopoly experimentation of learning with simulated markets. Journal of Economic Behavior & Organization 35 (3): 333–355.Google Scholar
  31. Greenwald, A.R., and J.O. Kephart. 1999. Shopbots and pricebots. In Agent mediated electronic commerce II, ed. A. Moukas, C. Sierra, and F. Ygge, 1–23. Berlin: Springer.Google Scholar
  32. Harrington, J.E. 1995. Experimentation and learning in a differentiated-products duopoly. Journal of Economic Theory 66 (1): 275–288.Google Scholar
  33. Harrison, J.M., N.B. Keskin, and A. Zeevi. 2012. Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Science 58 (3): 570–586.Google Scholar
  34. Isler, K., and H. Imhof. 2008. A game theoretic model for airline revenue management and competitive pricing. Journal of Revenue and Pricing Management 7 (4): 384–396.Google Scholar
  35. Johnson Ferreira, K., D. Simchi-Levi, and H. Wang. 2016. Online network revenue management using Thompson sampling. Working paper, Accessed 23 August 2018.
  36. Jumadinova, J., and P. Dasgupta. 2008. Firefly-inspired synchronization for improved dynamic pricing in online markets. In Self-Adaptive and Self-Organizing Systems, 2008. SASO ’08. Second IEEE International Conference on, IEEE, pp. 403–412.Google Scholar
  37. Jumadinova, J., and P. Dasgupta. 2010. Multi-attribute regret-based dynamic pricing. In Agent-mediated electronic commerce and trading agent design and analysis. Lecture notes in business information processing, vol. 44, eds. W. Ketter, H. La Poutré, N. Sadeh, O. Shehory, and W. Walsh, 73–87. Berlin: Springer.Google Scholar
  38. Keller, G., and S. Rady. 2003. Price dispersion and learning in a dynamic differentiated-goods duopoly. The RAND Journal of Economics 34 (1): 138–165.Google Scholar
  39. Keskin, N.B., and A. Zeevi. 2014. Dynamic pricing with an unknown demand model: Asymptotically optimal semi-myopic policies. Operations Research 62 (5): 1142–1167.Google Scholar
  40. Kirman, A. 1983. On mistaken beliefs and resultant equilibria. In Individual forecasting and aggregate outcomes, ed. R. Frydman, and E.S. Phelps, 147–166. New York: Cambridge University Press.Google Scholar
  41. Kirman, A.P. 1975. Learning by firms about demand conditions. In Adaptive economics, ed. R.H. Day, and T. Graves, 137–156. New York: Academic Press.Google Scholar
  42. Kirman, A.P. 1995. Learning in oligopoly: Theory, simulation, and experimental evidence. In Learning and rationality in economics, ed. A.P. Kirman, and M. Salmon, 127–178. Cambridge, MA: Basil Blackwell.Google Scholar
  43. Könönen, V. 2006. Dynamic pricing based on asymmetric multiagent reinforcement learning. International Journal of Intelligent Systems 21 (1): 73–98.Google Scholar
  44. Kutschinski, E., T. Uthmann, and D. Polani. 2003. Learning competitive pricing strategies by multi-agent reinforcement learning. Journal of Economic Dynamics and Control 27 (11–12): 2207–2218.Google Scholar
  45. Kwon, C., T.L. Friesz, R. Mookherjee, T. Yao, and B. Feng. 2009. Non-cooperative competition among revenue maximizing service providers with demand learning. European Journal of Operational Research 197 (3): 981–996.Google Scholar
  46. Li, J., T. Yao, and H. Gao. 2010. A revenue maximizing strategy based on Bayesian analysis of demand dynamics. In Proceedings of the 2009 SIAM conference on mathematics for industry, society for industrial and applied mathematics, eds. D.A. Field, and T.J. Peters, 174–181. Philadelphia.Google Scholar
  47. Mirman, L.J., L. Samuelson, and A. Urbano. 1993. Duopoly signal jamming. Economic Theory 3 (1): 129–149.Google Scholar
  48. Perakis, G., and A. Sood. 2006. Competitive multi-period pricing for perishable products: A robust optimization approach. Mathematical Programming 107 (1): 295–335.Google Scholar
  49. Ramezani, S., Bosman, P. A. N. and H. La Poutre. 2011. Adaptive strategies for dynamic pricing agents. In 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology IEEE, pp. 323–328.Google Scholar
  50. Rassenti, S., S.S. Reynolds, V.L. Smith, and F. Szidarovszky. 2000. Adaptation and convergence of behavior in repeated experimental Cournot games. Journal of Economic Behavior & Organization 41 (2): 117–146.Google Scholar
  51. Schinkel, M.P., J. Tuinstra, and D. Vermeulen. 2002. Convergence of Bayesian learning to general equilibrium in mis-specified models. Journal of Mathematical Economics 38 (4): 483–508.Google Scholar
  52. Sutton, R.S., and A.G. Barto. 1998. Reinforcement learning: An introduction, vol. 1. Cambridge: MIT Press.Google Scholar
  53. Tesauro, G., and J.O. Kephart. 2002. Pricing in agent economies using multi-agent Q-learning. Autonomous Agents and Multi-Agent Systems 5 (1): 289–304.Google Scholar
  54. Tuinstra, J. 2004. A price adjustment process in a model of monopolistic competition. International Game Theory Review 6 (3): 417–442.Google Scholar

Copyright information

© Springer Nature Limited 2018

Authors and Affiliations

  • Ruben van de Geer
    • 1
    Email author
  • Arnoud V. den Boer
    • 2
    • 3
  • Christopher Bayliss
    • 4
  • Christine S. M. Currie
    • 5
  • Andria Ellina
    • 5
  • Malte Esders
    • 6
  • Alwin Haensel
    • 7
  • Xiao Lei
    • 8
  • Kyle D. S. Maclean
    • 9
  • Antonio Martinez-Sykora
    • 5
  • Asbjørn Nilsen Riseth
    • 10
  • Fredrik Ødegaard
    • 9
  • Simos Zachariades
    • 5
  1. 1.Department of MathematicsVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Amsterdam Business SchoolUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.IN3 - Computer Science DepartmentUniversitat Oberta de CatalunyaBarcelonaSpain
  5. 5.Mathematical SciencesUniversity of SouthamptonSouthamptonUK
  6. 6.Faculty IV Electrical Engineering and Computer ScienceTechnische Universität BerlinBerlinGermany
  7. 7.Haensel AMS, Advanced Mathematical SolutionsBerlinGermany
  8. 8.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  9. 9.Ivey Business SchoolWestern UniversityLondonCanada
  10. 10.Mathematical InstituteUniversity of OxfordOxfordUK

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