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The Stability of Price Dispersion under Seller and Consumer Learning

Author

Listed:
  • Ed Hopkins

    (University of Edinburgh)

  • Roberty M. Seymour

    (University College, London)

Abstract

In many markets it is possible to find rival sellers charging different prices for the same good. Earlier research has attempted to explain this phenomenon by demonstrating the existence of dispersed price equilibria when consumers must make use of costly search to discover prices. We ask whether such equilibria can be learnt when sellers adjust prices adaptively in response to current market conditions. With consumer behaviour fixed, convergence to a dispersed price equilibrium is possible in some cases. However, once consumer learning is introduced, the monopoly outcome first found by Diamond (1971) is the only stable equilibrium.

Suggested Citation

  • Ed Hopkins & Roberty M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," Game Theory and Information 0203002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0203002
    Note: Type of Document - pdf; prepared on PC; pages: 36; figures: included
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    References listed on IDEAS

    as
    1. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
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    3. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
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    6. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    7. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    8. Rothschild, Michael, 1973. "Models of Market Organization with Imperfect Information: A Survey," Journal of Political Economy, University of Chicago Press, vol. 81(6), pages 1283-1308, Nov.-Dec..
    9. 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.
    10. 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.
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    Citations

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    Cited by:

    1. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.
    2. Morgan, John & Orzen, Henrik & Sefton, Martin, 2006. "An experimental study of price dispersion," Games and Economic Behavior, Elsevier, vol. 54(1), pages 134-158, January.
    3. Timothy N. Cason & Shakun D. Mago, 2010. "COSTLY BUYER SEARCH IN LABORATORY MARKETS WITH SELLER ADVERTISING -super-," Journal of Industrial Economics, Wiley Blackwell, vol. 58(2), pages 424-449, June.
    4. Hoffmann, Eric, 2016. "On the learning and stability of mixed strategy Nash equilibria in games of strategic substitutes," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 349-362.
    5. 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.
    6. Ed Hopkins, 2002. "Adaptive Learning Models of Consumer Behaviour (first version)," ESE Discussion Papers 80, Edinburgh School of Economics, University of Edinburgh.
    7. Hopkins, Ed, 2007. "Adaptive learning models of consumer behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 348-368.
    8. García-Gallego, Aurora & Georgantzís, Nikolaos & Jaramillo-Gutiérrez, Ainhoa & Pereira, Pedro & Pernías-Cerrillo, J. Carlos, 2014. "On the evolution of monopoly pricing in Internet-assisted search markets," Journal of Business Research, Elsevier, vol. 67(5), pages 795-801.
    9. Kováč, Eugen & Schmidt, Robert C., 2014. "Market share dynamics in a duopoly model with word-of-mouth communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 178-206.
    10. Klaus Adam, 2001. "Competitive Prices in Markets with Search and Information Frictions," CSEF Working Papers 55, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    11. Edoardo Gaffeo & Mauro Gallegati & Umberto Gostoli, 2012. "An agent-based "proof of principle" for Walrasian macroeconomic theory," CEEL Working Papers 1202, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    12. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    13. repec:eee:jeborg:v:137:y:2017:i:c:p:339-360 is not listed on IDEAS
    14. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," Levine's Bibliography 321307000000000724, UCLA Department of Economics.
    15. repec:eee:dyncon:v:84:y:2017:i:c:p:32-42 is not listed on IDEAS
    16. 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.
    17. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April.
    18. Rauh, Michael T., 2009. "Strategic complementarities and search market equilibrium," Games and Economic Behavior, Elsevier, vol. 66(2), pages 959-978, July.
    19. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    20. Timothy N. Cason & Shakun Datta, 2008. "Costly Buyer Search in Laboratory Markets with Seller Advertising," Purdue University Economics Working Papers 1212, Purdue University, Department of Economics.
    21. 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.
    22. Lahkar, Ratul & Riedel, Frank, 2016. "The Continuous Logit Dynamic and Price Dispersion," Center for Mathematical Economics Working Papers 521, Center for Mathematical Economics, Bielefeld University.
    23. Robert Jump, 2016. "Evolutionary learning and the stability of wage posting equilibria," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1117-1135, December.

    More about this item

    Keywords

    Learning; Evolution; Search; Price Dispersion;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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