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Poisson Price Dispersion

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  • Halevy, Yoram
  • Michtaich, Igal

Abstract

We study a competitive market for a homogeneous good, in which the only uncertainty concerns the number of identical sellers, who are sampled by a finite Poisson process from a continuum of potential participants. It is shown that, in equilibrium, there is price dispersion. Specifically, prices conform to a Poisson process on an interval, which is a proper subset of that between the sellers' cost and the buyers' reservation price. Although prices arbitrarily close to the latter may occur in equilibrium, they are less frequent than prices at the lower end of the pricing interval.

Suggested Citation

  • Halevy, Yoram & Michtaich, Igal, 2005. "Poisson Price Dispersion," Microeconomics.ca working papers halevy-05-07-26-12-10-45, Vancouver School of Economics, revised 25 Feb 2014.
  • Handle: RePEc:ubc:pmicro:halevy-05-07-26-12-10-45
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    File URL: http://faculty.arts.ubc.ca/yhalevy/poisson.pdf
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    References listed on IDEAS

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    1. Eden, Benjamin, 1990. "Marginal Cost Pricing When Spot Markets Are Complete," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1293-1306, December.
    2. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    3. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
    4. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    5. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-1127, September.
    6. Michael Peters, 1985. "Immobility, Rationing and Price Competition," Review of Economic Studies, Oxford University Press, vol. 52(4), pages 593-604.
    7. Michael Peters & Ralph A. Winter, 1983. "Market Equilibrium and the Resolution of Uncertainty," Canadian Journal of Economics, Canadian Economics Association, vol. 16(3), pages 381-390, August.
    8. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    9. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
    10. James D. Dana Jr., 1999. "Equilibrium Price Dispersion Under Demand Uncertainty: The Roles of Costly Capacity and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 632-660, Winter.
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    More about this item

    Keywords

    Random-player games; Poisson games; Uncertain number of sellers; Directed search.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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