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From Imitation to Collusion: Long-run Learning in a Low-Information Environment

  • Daniel Friedman
  • Steffen Huck
  • Ryan Oprea
  • Simon Weidenholzer

We explore the stability of imitation in a 1200-period experimental Cournot game where subjects do not know the payoff function but see the output quantities and payoffs of each oligopolist after every period. In line with theoretical predictions and previous experimental findings, our oligopolies reach highly competitive levels within 50 periods. However, already after 100 periods, quantities start to drop and eventually fall deep into collusive territory without pausing at the Nash equilibrium. Our results demonstrate how groups of subjects can learn their way out of dysfunctional heuristics, and suggest elements for a new theory of how cooperation emerges.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000457.

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Date of creation: 22 Jul 2012
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Handle: RePEc:cla:levarc:786969000000000457
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  1. 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.
  2. Bigoni, Maria & Casari, Marco & Skrzypacz, Andrzej & Spagnolo, Giancarlo, 2013. "Time Horizon and Cooperation in Continuous Time," Research Papers 2088r, Stanford University, Graduate School of Business.
  3. Steffen Huck & Hans-Theo Normann & Jörg Oechssler, 2001. "Two are Few and Four are Many: Number Effects in Experimental Oligopolies," Bonn Econ Discussion Papers bgse12_2001, University of Bonn, Germany.
  4. Apestgeguia, Jose & Huck, Steffen & Oechssler, Jörg, 2005. "Imitation - Theory and Experimental Evidence," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 54, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  5. Antoni Bosch-Domènech & Nicolaas J. Vriend, 1998. "Imitation of succesful behavior in Cournot markets," Economics Working Papers 269, Department of Economics and Business, Universitat Pompeu Fabra, revised May 1999.
  6. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
  7. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  8. G. Ellison & D. Fudenberg, 2010. "Rules of Thumb for Social Learning," Levine's Working Paper Archive 435, David K. Levine.
  9. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
  10. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
  11. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  12. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  13. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
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  15. Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Other publications TiSEM a6a771c5-31ba-4193-8f76-a, Tilburg University, School of Economics and Management.
  16. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
  17. James Pettit & Daniel Friedman & Curtis Kephart & Ryan Oprea, 2014. "Software for continuous game experiments," Experimental Economics, Springer, vol. 17(4), pages 631-648, December.
  18. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information 9707009, EconWPA, revised 22 Jul 1997.
  19. Daniel Friedman & Ryan Oprea, 2012. "A Continuous Dilemma," American Economic Review, American Economic Association, vol. 102(1), pages 337-63, February.
  20. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 973-997.
  21. Siegfried Berninghaus & Karl-Martin Ehrhart & Claudia Keser, 1999. "Continuous-Time Strategy Selection in Linear Population Games," Experimental Economics, Springer, vol. 2(1), pages 41-57, August.
  22. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  23. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 2004. "Through Trial and Error to Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(1), pages 205-224, 02.
  24. Ben Greiner, 2004. "The Online Recruitment System ORSEE 2.0 - A Guide for the Organization of Experiments in Economics," Working Paper Series in Economics 10, University of Cologne, Department of Economics.
  25. Paul Milgrom & John Roberts, 2010. "Adaptive and Sophisticated Learning in Repeated Normal-Form Games," Levine's Working Paper Archive 418, David K. Levine.
  26. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-79, March.
  27. Dan Alger, 1987. "Laboratory Tests of Equilibrium Predictions with Disequilibrium Data," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 105-145.
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