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The Stability of Price Dispersion under Seller and Consumer Learning

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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

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Steven Salop & Joseph Stiglitz, 1977. "Bargains and Ripoffs: A Model of Monopolistically Competitive Price Dispersion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 493-510.
    4. 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.
    5. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    6. JÃrg Oechssler & Frank Riedel, 2001. "Evolutionary dynamics on infinite strategy spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 141-162.
    7. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    8. Wilde, Louis L, 1992. "Comparison Shopping as a Simultaneous Move Game," Economic Journal, Royal Economic Society, vol. 102(412), pages 562-569, May.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    11. Erik Brynjolfsson & Michael D. Smith, 2000. "Frictionless Commerce? A Comparison of Internet and Conventional Retailers," Management Science, INFORMS, vol. 46(4), pages 563-585, April.
    12. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    13. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    14. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    15. 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..
    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. 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.
    18. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
    19. Benabou Roland, 1993. "Search Market Equilibrium, Bilateral Heterogeneity, and Repeat Purchases," Journal of Economic Theory, Elsevier, vol. 60(1), pages 140-158, June.
    20. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    21. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
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    More about this item

    Keywords

    Learning; Evolution; Search; Price Dispersion;
    All these keywords.

    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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