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Evolving Rules: Imitation and Best Response Learning in Cournot Oligopoly

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  • Xiaomeng Ding
  • Simon Weidenholzer
  • Boyu Zhang

Abstract

We study evolutionary dynamics in which firms endogenously revise the behavioral rules that govern strategy revisions in symmetric Cournot oligopoly. Specifically, we consider two principles that guide rule revision, No-Birth and Survival-of-the-Fittest, both grounded in imitation-based heuristics. We show that, under these principles, all firms eventually adopt the same behavioral rule. Focusing on two classical rules, myopic best response and imitation, we demonstrate that rule revision plays a crucial role in determining long-run equilibria in Cournot oligopoly. The set of long-run equilibria includes the state where all players use best response learning and choose the Nash equilibrium quantities and states where all firms use imitation learning and choose specific symmetric quantities which include (but are not necessarily restricted to) Walrasian quantities. Our results extend to more general aggregative games.

Suggested Citation

  • Xiaomeng Ding & Simon Weidenholzer & Boyu Zhang, 2025. "Evolving Rules: Imitation and Best Response Learning in Cournot Oligopoly," Papers 2511.09839, arXiv.org.
  • Handle: RePEc:arx:papers:2511.09839
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    1. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.
    2. Alex Possajennikov, 2003. "Evolutionary foundations of aggregate-taking behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 921-928, June.
    3. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    4. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 407-430, June.
    5. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    6. Bigoni, Maria & Fort, Margherita, 2013. "Information and learning in oligopoly: An experiment," Games and Economic Behavior, Elsevier, vol. 81(C), pages 192-214.
    7. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    8. Friedman, Daniel & Huck, Steffen & Oprea, Ryan & Weidenholzer, Simon, 2015. "From imitation to collusion: Long-run learning in a low-information environment," Journal of Economic Theory, Elsevier, vol. 155(C), pages 185-205.
    9. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    10. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
    11. Steffen Huck & Hans-Theo Normann & Jörg Oechssler, 2002. "Stability of the Cournot process - experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 123-136.
    12. Jaromír Kovářík & Friederike Mengel & José Gabriel Romero, 2018. "Learning in network games," Quantitative Economics, Econometric Society, vol. 9(1), pages 85-139, March.
    13. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    14. Huck, Steffen & Leutgeb, Johannes & Oprea, Ryan, 2017. "Payoff information hampers the evolution of cooperation," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 8, pages 1-1.
    15. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    16. Alós-Ferrer, Carlos & Ritschel, Alexander, 2021. "Multiple behavioral rules in Cournot oligopolies," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 250-267.
    17. Apesteguia, Jose & Huck, Steffen & Oechssler, Jörg & Weidenholzer, Simon, 2010. "Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1603-1617, September.
    18. Bossan, Benjamin & Jann, Ole & Hammerstein, Peter, 2015. "The evolution of social learning and its economic consequences," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 266-288.
    19. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    20. Weisbach, Michael S., 1995. "CEO turnover and the firm's investment decisions," Journal of Financial Economics, Elsevier, vol. 37(2), pages 159-188, February.
    21. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," LSE Research Online Documents on Economics 68714, London School of Economics and Political Science, LSE Library.
    22. Conlisk, John, 1980. "Costly optimizers versus cheap imitators," Journal of Economic Behavior & Organization, Elsevier, vol. 1(3), pages 275-293, September.
    23. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," Journal of Economic Behavior & Organization, Elsevier, vol. 127(C), pages 1-15.
    24. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 471-477, August.
    25. Ryan Oprea, 2021. "What Makes a Rule Complex? Erratum," American Economic Review, American Economic Association, vol. 111(2), pages 755-755, February.
    26. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    27. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    28. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    29. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
    30. Jörg Oechssler & Alex Roomets & Stefan Roth, 2016. "From imitation to collusion: a replication," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 2(1), pages 13-21, May.
    31. Xiaochen Wang & Lei Zhou & Alex McAvoy & Aming Li, 2023. "Imitation dynamics on networks with incomplete information," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    32. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    33. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2006. "Imitation, local interactions, and efficiency," Economics Letters, Elsevier, vol. 93(2), pages 163-168, November.
    34. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    35. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2014. "Imitation and the role of information in overcoming coordination failures," Games and Economic Behavior, Elsevier, vol. 87(C), pages 397-411.
    36. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    37. Antoni Bosch-DomËnech & Nicolaas J. Vriend, 2003. "Imitation of successful behaviour in cournot markets," Economic Journal, Royal Economic Society, vol. 113(487), pages 495-524, April.
    38. Juang, W-T. & Sabourian, H., 2021. "Rules and Mutation - A Theory of How Efficiency and Rawlsian Egalitarianism/Symmetry May Emerge," Cambridge Working Papers in Economics 2101, Faculty of Economics, University of Cambridge.
    39. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
    40. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    41. repec:hal:pseose:halshs-01157537 is not listed on IDEAS
    42. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages 80-95, March.
    43. Franklin M. Fisher, 1961. "The Stability of the Cournot Oligopoly Solution: The Effects of Speeds of Adjustment and Increasing Marginal Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 125-135.
    44. Denis, David J & Denis, Diane K, 1995. "Performance Changes Following Top Management Dismissals," Journal of Finance, American Finance Association, vol. 50(4), pages 1029-1057, September.
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