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Cournot Meets Bayes-Nash: A Discontinuity in Behavior in Finitely Repeated Duopoly Games

Author

Listed:
  • Cédric Argenton

    (CentER & TILEC, Tilburg University)

  • Radosveta Ivanova-Stenzel

    (TU Berlin)

  • Wieland Müller

    (VCEE, University of Vienna, CentER & TILEC, Tilburg University)

Abstract

We conduct a series of Cournot duopoly market experiments with a high number of repetitions and fixed matching. Our treatments include markets with (a) complete cost symmetry and complete information, (b) slight cost asymmetry and complete information, and (c) varying cost asymmetries and incomplete information. For the case of complete cost symmetry and complete information, our data confirm the well-known result that duopoly players achieve, on average, partial collusion. However, as soon as any level of cost asymmetry or incomplete information is introduced, observed average individual quantities are remarkably close to the static Bayes-Nash equilibrium predictions.

Suggested Citation

  • Cédric Argenton & Radosveta Ivanova-Stenzel & Wieland Müller, 2023. "Cournot Meets Bayes-Nash: A Discontinuity in Behavior in Finitely Repeated Duopoly Games," Rationality and Competition Discussion Paper Series 460, CRC TRR 190 Rationality and Competition.
  • Handle: RePEc:rco:dpaper:460
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    1. Vincent P. Crawford & Uri Gneezy & Yuval Rottenstreich, 2008. "The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures," American Economic Review, American Economic Association, vol. 98(4), pages 1443-1458, September.
    2. Katerina Sherstyuk, 1999. "Collusion Without Conspiracy: An Experimental Study of One-Sided Auctions," Experimental Economics, Springer;Economic Science Association, vol. 2(1), pages 59-75, August.
    3. Till Requate & Israel Waichman, 2011. "“A profit table or a profit calculator?” A note on the design of Cournot oligopoly experiments," Experimental Economics, Springer;Economic Science Association, vol. 14(1), pages 36-46, March.
    4. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 973-997.
    5. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 2000. "Does information about competitors' actions increase or decrease competition in experimental oligopoly markets?," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 39-57, January.
    6. Jan Potters & Sigrid Suetens, 2009. "Cooperation in Experimental Games of Strategic Complements and Substitutes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1125-1147.
    7. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 2004. "Two are few and four are many: number effects in experimental oligopolies," Journal of Economic Behavior & Organization, Elsevier, vol. 53(4), pages 435-446, April.
    8. Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 509-551.
    9. 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.
    10. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    11. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    12. Subir K. Chakrabarti, 2010. "Collusive Equilibrium In Cournot Oligopolies With Unknown Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(4), pages 1209-1238, November.
    13. Rassenti, Stephen & Reynolds, Stanley S. & Smith, Vernon L. & Szidarovszky, Ferenc, 2000. "Adaptation and convergence of behavior in repeated experimental Cournot games," Journal of Economic Behavior & Organization, Elsevier, vol. 41(2), pages 117-146, February.
    14. Mermer, Ayşe Gül & Müller, Wieland & Suetens, Sigrid, 2021. "Cooperation in infinitely repeated games of strategic complements and substitutes," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 1191-1205.
    15. Christoph Engel, 2007. "How Much Collusion? A Meta-Analysis Of Oligopoly Experiments," Journal of Competition Law and Economics, Oxford University Press, vol. 3(4), pages 491-549.
    16. 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.
    17. Raab, Philippe & Schipper, Burkhard C., 2009. "Cournot competition between teams: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 72(2), pages 691-702, November.
    18. 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.
    19. Douglas Davis & Robert Reilly & Bart Wilson, 2003. "Cost Structures and Nash Play in Repeated Cournot Games," Experimental Economics, Springer;Economic Science Association, vol. 6(2), pages 209-226, October.
    20. Davies, Stephen & Olczak, Matthew & Coles, Heather, 2011. "Tacit collusion, firm asymmetries and numbers: Evidence from EC merger cases," International Journal of Industrial Organization, Elsevier, vol. 29(2), pages 221-231, March.
    21. Klaus Abbink & Jordi Brandts, 2005. "Price Competition Under Cost Uncertainty: A Laboratory Analysis," Economic Inquiry, Western Economic Association International, vol. 43(3), pages 636-648, July.
    22. Maria Bigoni & Jan Potters & Giancarlo Spagnolo, 2019. "Frequency of interaction, communication and collusion: an experiment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 827-844, November.
    23. Hans-Theo Normann & Till Requate & Israel Waichman, 2014. "Do short-term laboratory experiments provide valid descriptions of long-term economic interactions? A study of Cournot markets," Experimental Economics, Springer;Economic Science Association, vol. 17(3), pages 371-390, September.
    24. T. Ahn & Myungsuk Lee & Lore Ruttan & James Walker, 2007. "Asymmetric payoffs in simultaneous and sequential prisoner’s dilemma games," Public Choice, Springer, vol. 132(3), pages 353-366, September.
    25. Charles F. Mason & Owen R. Phillips, 1997. "Information And Cost Asymmetry In Experimental Duopoly Markets," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 290-299, May.
    26. Sherstyuk, Katerina, 2002. "Collusion in private value ascending price auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 48(2), pages 177-195, June.
    27. Sigrid Suetens & Jan Potters, 2007. "Bertrand colludes more than Cournot," Experimental Economics, Springer;Economic Science Association, vol. 10(1), pages 71-77, March.
    28. Maria Bigoni & Jan Potters & Giancarlo Spagnolo, 2019. "Frequency of interaction, communication and collusion: an experiment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 827-844, November.
    29. Mason, Charles F & Phillips, Owen R & Nowell, Clifford, 1992. "Duopoly Behavior in Asymmetric Markets: An Experimental Evaluation," The Review of Economics and Statistics, MIT Press, vol. 74(4), pages 662-670, November.
    30. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    31. Noussair, Charles N. & Seres, Gyula, 2020. "The effect of collusion on efficiency in experimental auctions," Games and Economic Behavior, Elsevier, vol. 119(C), pages 267-287.
    32. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    33. Davis, Douglas D., 2002. "Strategic interactions, market information and predicting the effects of mergers in differentiated product markets," International Journal of Industrial Organization, Elsevier, vol. 20(9), pages 1277-1312, November.
    34. Andreoni, James & Che, Yeon-Koo & Kim, Jinwoo, 2007. "Asymmetric information about rivals' types in standard auctions: An experiment," Games and Economic Behavior, Elsevier, vol. 59(2), pages 240-259, May.
    35. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    36. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    37. Pedro Dal Bó & Guillaume R. Fréchette, 2018. "On the Determinants of Cooperation in Infinitely Repeated Games: A Survey," Journal of Economic Literature, American Economic Association, vol. 56(1), pages 60-114, March.
    38. 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.
    39. Waichman, Israel & Requate, Till & Siang, Ch’ng Kean, 2014. "Communication in Cournot competition: An experimental study," Journal of Economic Psychology, Elsevier, vol. 42(C), pages 1-16.
    40. Fischer, Christian & Normann, Hans-Theo, 2019. "Collusion and bargaining in asymmetric Cournot duopoly—An experiment," European Economic Review, Elsevier, vol. 111(C), pages 360-379.
    41. Anthony M. Kwasnica & Katerina Sherstyuk, 2007. "Collusion and Equilibrium Selection in Auctions," Economic Journal, Royal Economic Society, vol. 117(516), pages 120-145, January.
    42. 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.
    43. Fonseca, Miguel A. & Normann, Hans-Theo, 2012. "Explicit vs. tacit collusion—The impact of communication in oligopoly experiments," European Economic Review, Elsevier, vol. 56(8), pages 1759-1772.
    44. Yoella Bereby-Meyer & Alvin E. Roth, 2006. "The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation," American Economic Review, American Economic Association, vol. 96(4), pages 1029-1042, September.
    45. Christopher Avery & John H. Kagel, 1997. "Second‐Price Auctions with Asymmetric Payoffs: An Experimental Investigation," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(3), pages 573-603, September.
    46. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    47. Guth, Werner & Ivanova-Stenzel, Radosveta & Wolfstetter, Elmar, 2005. "Bidding behavior in asymmetric auctions: An experimental study," European Economic Review, Elsevier, vol. 49(7), pages 1891-1913, October.
    48. Altavilla, Carlo & Luini, Luigi & Sbriglia, Patrizia, 2006. "Social learning in market games," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 632-652, December.
    49. Mason, Charles F. & Phillips, Owen R. & Redington, Douglas B., 1991. "The role of gender in a non-cooperative game," Journal of Economic Behavior & Organization, Elsevier, vol. 15(2), pages 215-235, March.
    50. Feinberg, Robert M & Husted, Thomas A, 1993. "An Experimental Test of Discount-Rate Effects on Collusive Behaviour in Duopoly Markets," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 153-160, June.
    51. Hu, Audrey & Offerman, Theo & Onderstal, Sander, 2011. "Fighting collusion in auctions: An experimental investigation," International Journal of Industrial Organization, Elsevier, vol. 29(1), pages 84-96, January.
    52. Friederike Mengel, 2018. "Risk and Temptation: A Meta‐study on Prisoner's Dilemma Games," Economic Journal, Royal Economic Society, vol. 128(616), pages 3182-3209, December.
    53. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    54. Roberts, Kevin, 1985. "Cartel Behaviour and Adverse Selection," Journal of Industrial Economics, Wiley Blackwell, vol. 33(4), pages 401-413, June.
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    More about this item

    Keywords

    Cournot; Bayesian game; Bayes-Nash equilibrium; repeated games; collusion; cooperation; experimental economics;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

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