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Price dispersion in pure strategies

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  • Kozin, Georgii
  • Suzdaltsev, Alex

Abstract

We revisit Anderson and de Palma (2005)’s model of firm pricing when searching consumers follow simple reservation price rules. In this model, any pure-strategy equilibrium, if exists, features different prices set by identical firms, i.e., price dispersion may arise without randomization. However, the existence of such an equilibrium has not been established beyond simple examples as profit functions in this model are naturally not quasiconcave. We show that in a duopoly a (dispersed) pure-strategy equilibrium always exists—despite the non-quasiconcavity—under any reservation price distribution with monotone hazard rate. This may help explain persistent price dispersion.

Suggested Citation

  • Kozin, Georgii & Suzdaltsev, Alex, 2026. "Price dispersion in pure strategies," Economics Letters, Elsevier, vol. 258(C).
  • Handle: RePEc:eee:ecolet:v:258:y:2026:i:c:s0165176525005798
    DOI: 10.1016/j.econlet.2025.112742
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    References listed on IDEAS

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    1. Alexei Parakhonyak & Anton Sobolev, 2015. "Non‐Reservation Price Equilibrium and Search without Priors," Economic Journal, Royal Economic Society, vol. 0(584), pages 887-909, May.
    2. 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.
    3. Stahl, Dale O., 1996. "Oligopolistic pricing with heterogeneous consumer search," International Journal of Industrial Organization, Elsevier, vol. 14(2), pages 243-268.
    4. Greg Kaplan & Guido Menzio, 2015. "The Morphology Of Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1165-1206, November.
    5. Zhou, Jidong, 2009. "Prominence and Consumer Search: The Case With Multiple Prominent Firms," MPRA Paper 12554, University Library of Munich, Germany.
    6. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    7. Arnold, Michael A, 2000. "Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 117-131, February.
    8. Simon P. Anderson & Regis Renault, 1999. "Pricing, Product Diversity, and Search Costs: A Bertrand-Chamberlin-Diamond Model," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 719-735, Winter.
    9. repec:bon:boncrc:crctr224_2025_644 is not listed on IDEAS
    10. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    11. Reinganum, Jennifer F, 1979. "A Simple Model of Equilibrium Price Dispersion," Journal of Political Economy, University of Chicago Press, vol. 87(4), pages 851-858, August.
    12. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1415-1464.
    13. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    14. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 1992. "It takes two to tango: Equilibria in a model of sales," Games and Economic Behavior, Elsevier, vol. 4(4), pages 493-510, October.
    15. Greg Kaplan & Guido Menzio, 2015. "The Morphology Of Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1165-1206, November.
    16. David P. Myatt & David Ronayne, 2025. "Finding a Good Deal: Stable Prices, Costly Search, and the Effect of Entry," Rationality and Competition Discussion Paper Series 524, CRC TRR 190 Rationality and Competition.
    17. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    18. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
    19. Zhou, Jidong, 2011. "Ordered search in differentiated markets," International Journal of Industrial Organization, Elsevier, vol. 29(2), pages 253-262, March.
    20. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    21. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    22. Simon P. Anderson & André De Palma, 2005. "Price Dispersion and Consumer Reservation Prices," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(1), pages 61-91, March.
    23. Mark Armstrong & John Vickers & Jidong Zhou, 2009. "Prominence and consumer search," RAND Journal of Economics, RAND Corporation, vol. 40(2), pages 209-233, June.
    24. Anderson, Simon P. & Renault, Regis, 2003. "Efficiency and surplus bounds in Cournot competition," Journal of Economic Theory, Elsevier, vol. 113(2), pages 253-264, December.
    25. Stahl, Dale O, II, 1989. "Oligopolistic Pricing with Sequential Consumer Search," American Economic Review, American Economic Association, vol. 79(4), pages 700-712, September.
    26. Volker Nocke & Nicolas Schutz, 2025. "Oligopoly, Complementarities, and Transformed Potentials," CRC TR 224 Discussion Paper Series crctr224_2025_644_v2, University of Bonn and University of Mannheim, Germany, revised Jul 2025.
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