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Learning and Noisy Equilibrium Behavior in an Experimental Study of Imperfect Price Competition

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  • C. Monica Capra
  • Jacob K. Goeree

    ()

  • Rosario Gomez
  • Charles A. Holt

    ()

Abstract

This paper considers a duopoly price-choice game in which the unique Nash equilibrium is the Bertrand outcome. Price competition, however, is imperfect in the sense that the market share of the high-price firm is not zero. Economic intuition suggests that price levels should be positively related to the market share of the high-price firm. Although this relationship is not predicted by standard game theory, it is implied by a generalization of the Nash equilibrium that results when players make noisy (logit) best responses to expected payoff differences. This logit equilibrium model was used to design a laboratory experiment with treatments that correspond to changing the market share of the high-price firm. The model predicts the final-period price averages for both treatments with remarkable accuracy. Moreover computer simulations of a naive learning model were used, ex ante, to predict the observed differences in the time paths of average prices.

Suggested Citation

  • C. Monica Capra & Jacob K. Goeree & Rosario Gomez & Charles A. Holt, 2000. "Learning and Noisy Equilibrium Behavior in an Experimental Study of Imperfect Price Competition," Virginia Economics Online Papers 336, University of Virginia, Department of Economics.
  • Handle: RePEc:vir:virpap:336
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    References listed on IDEAS

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    Cited by:

    1. C. Monica Capra & Susana Cabrera & Rosario Gómez, 2003. "The Effects of Common Advice on One-shot Traveler’s Dilemma Games: Explaining Behavior through an Introspective Model with Errors," Economic Working Papers at Centro de Estudios Andaluces E2003/17, Centro de Estudios Andaluces.
    2. Schmutzler, Armin, 2011. "A unified approach to comparative statics puzzles in experiments," Games and Economic Behavior, Elsevier, vol. 71(1), pages 212-223, January.
    3. Susana Cabrera & C. Monica Capra & Rosario Gomez, 2005. "Introspection in One-shot Traveler's Dilemma Games," Emory Economics 0504, Department of Economics, Emory University (Atlanta).
    4. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    5. Ispano, Alessandro & Schwardmann, Peter, 2017. "Cooperating over losses and competing over gains: A social dilemma experiment," Games and Economic Behavior, Elsevier, vol. 105(C), pages 329-348.
    6. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    7. Ed Hopkins, 2002. "Adaptive Learning Models of Consumer Behaviour (first version)," ESE Discussion Papers 80, Edinburgh School of Economics, University of Edinburgh.
    8. Kubler, Dorothea & Muller, Wieland, 2002. "Simultaneous and sequential price competition in heterogeneous duopoly markets: experimental evidence," International Journal of Industrial Organization, Elsevier, vol. 20(10), pages 1437-1460, December.
    9. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    10. Patrick Bajari & Ali Hortacsu, 2005. "Are Structural Estimates of Auction Models Reasonable? Evidence from Experimental Data," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 703-741, August.
    11. Subhasish Dugar & Arnab Mitra, 2016. "Bertrand Competition With Asymmetric Marginal Costs," Economic Inquiry, Western Economic Association International, vol. 54(3), pages 1631-1647, July.
    12. Brit Grosskopf & Ido Erev & Eldad Yechiam, 2006. "Foregone with the Wind: Indirect Payoff Information and its Implications for Choice," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 285-302, August.
    13. Peeters, Ronald & Strobel, Martin, 2009. "Pricing behavior in asymmetric markets with differentiated products," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 24-32, January.
    14. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October.
    15. Charles A. Holt & Jacob K. Goeree, 1999. "Stochastic Game Theory: For Playing Games, Not Just for Doing Theory," Virginia Economics Online Papers 306, University of Virginia, Department of Economics.
    16. Susana Cabrera & C. Capra & Rosario Gómez, 2007. "Behavior in one-shot traveler’s dilemma games: model and experiments with advice," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(2), pages 129-152, June.
    17. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    18. Enrique Fatas & Juan Mañez, 2007. "Are low-price promises collusion guarantees? An experimental test of price matching policies," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(1), pages 59-77, March.
    19. Olivier Armantier & Nicolas Treich, 2006. "Overbidding in Independant Private-Values Auctions and Misperception of Probabilities," CIRANO Working Papers 2006s-15, CIRANO.
    20. Timothy Cason & Daniel Friedman, 1999. "Learning in a Laboratory Market with Random Supply and Demand," Experimental Economics, Springer;Economic Science Association, vol. 2(1), pages 77-98, August.
    21. Ralph-C. Bayer & Hang Wu, 2013. "Number of Sellers and Quantal Response Equilibrium Prices," School of Economics Working Papers 2013-15, University of Adelaide, School of Economics.
    22. Goeree, Jacob K. & Holt, Charles A. & Smith, Angela M., 2017. "An experimental examination of the volunteer's dilemma," Games and Economic Behavior, Elsevier, vol. 102(C), pages 303-315.
    23. Roger Waldeck & Eric Darmon, 2006. "Can boundedly rational sellers learn to play Nash?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(2), pages 147-169, November.
    24. Gabriel Galand, 2009. "The Neutrality of Money Revisited with a Bottom-Up Approach: Decentralisation, Limited Information and Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 33(4), pages 337-360, May.

    More about this item

    Keywords

    laboratory experiments; simulation; decision error; learning; logit equilibrium.;

    JEL classification:

    • 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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