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Dynamic Limit Pricing

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  • Toxvaerd, Flavio

Abstract

This paper studies a simple multi-period model of limit pricing under one-sided incomplete information. I characterize pooling and separating equilibria, determine conditions under which the latter exist and study under which conditions on the primitives the equilibria involve limit pricing. The results are compared to a static benchmark. I identify two regimes that depend on the primitives of the model, namely a monopoly price regime and a limit price regime. In the former, the unique reasonable equilibrium involves immediate separation on monopoly prices. In the latter, I identify a unique class of reasonable limit price equilibria in which different types may initially pool for an arbitrary amount of time and then (possibly) separate. I argue that in a reasonable equilibrium, all signaling takes place in a single period (if the informed player is able to do so). If separation occurs in finite time, this involves setting prices that are so low that the inefficient incumbent's profits from mimicking are strictly negative. With a sufficiently high discount factor, the losses from mimicking may become arbitrarily large.

Suggested Citation

  • Toxvaerd, Flavio, 2010. "Dynamic Limit Pricing," CEPR Discussion Papers 8104, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:8104
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    1. Milgrom, Paul & Roberts, John, 1982. "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica, Econometric Society, vol. 50(2), pages 443-459, March.
    2. Berck, Peter & Perloff, Jeffrey M., 1988. "The dynamic annihilation of a rational competitive fringe by a low-cost dominant firm," Journal of Economic Dynamics and Control, Elsevier, vol. 12(4), pages 659-678, November.
    3. Kamien, Morton I & Schwartz, Nancy L, 1971. "Limit Pricing and Uncertain Entry," Econometrica, Econometric Society, vol. 39(3), pages 441-454, May.
    4. Loretta J. Mester, 1992. "Perpetual Signalling with Imperfectly Correlated Costs," RAND Journal of Economics, The RAND Corporation, vol. 23(4), pages 548-563, Winter.
    5. Georg Noldeke & Eric van Damme, 1990. "Signalling in a Dynamic Labour Market," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 1-23.
    6. In-Koo Cho, 1990. "Uncertainty and Delay in Bargaining," Review of Economic Studies, Oxford University Press, vol. 57(4), pages 575-595.
    7. Therese Flaherty, M., 1980. "Dynamic limit pricing, barriers to entry, and rational firms," Journal of Economic Theory, Elsevier, vol. 23(2), pages 160-182, October.
    8. Kaya, Ayça, 2009. "Repeated signaling games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 841-854, July.
    9. Gaskins, Darius Jr., 1971. "Dynamic limit pricing: Optimal pricing under threat of entry," Journal of Economic Theory, Elsevier, vol. 3(3), pages 306-322, September.
    10. Vincent, Daniel R, 1998. "Repeated Signalling Games and Dynamic Trading Relationships," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 275-293, May.
    11. De Bondt, Raymond R, 1976. "Limit Pricing, Uncertain Entry, and the Entry Lag," Econometrica, Econometric Society, vol. 44(5), pages 939-946, September.
    12. Matthews, Steven A & Mirman, Leonard J, 1983. "Equilibrium Limit Pricing: The Effects of Private Information and Stochastic Demand," Econometrica, Econometric Society, vol. 51(4), pages 981-996, July.
    13. Weiss, Andrew, 1983. "A Sorting-cum-Learning Model of Education," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 420-442, June.
    14. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 179-221.
    15. Garth Saloner, 1984. "Dynamic Equilibrium Limit-Pricing in an Uncertain Environment," Working papers 342, Massachusetts Institute of Technology (MIT), Department of Economics.
    16. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    17. Rubinstein, Ariel, 1985. "A Bargaining Model with Incomplete Information about Time Preferences," Econometrica, Econometric Society, vol. 53(5), pages 1151-1172, September.
    18. Greg LeBlanc, 1992. "Signalling Strength: Limit Pricing and Predatory Pricing," RAND Journal of Economics, The RAND Corporation, vol. 23(4), pages 493-506, Winter.
    19. Judd, Kenneth L. & Petersen, Bruce C., 1986. "Dynamic limit pricing and internal finance," Journal of Economic Theory, Elsevier, vol. 39(2), pages 368-399, August.
    20. Heski Bar-Isaac, 2003. "Reputation and Survival: Learning in a Dynamic Signalling Model," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 231-251.
    21. Friedman, James W., 1983. "Limit price entry prevention when complete information is lacking," Journal of Economic Dynamics and Control, Elsevier, vol. 5(1), pages 187-199, February.
    22. Steven A. Lippman, 1980. "Optimal Pricing to Retard Entry," Review of Economic Studies, Oxford University Press, vol. 47(4), pages 723-731.
    23. Grossman, Sanford J. & Perry, Motty, 1986. "Sequential bargaining under asymmetric information," Journal of Economic Theory, Elsevier, vol. 39(1), pages 120-154, June.
    24. Baron, David P, 1973. "Limit Pricing, Potential Entry, and Barriers to Entry," American Economic Review, American Economic Association, vol. 63(4), pages 666-674, September.
    25. Madrigal, Vicente & Tan, Tommy C. C. & Werlang, Sergio Ribeiro da Costa, 1987. "Support restrictions and sequential equilibria," Journal of Economic Theory, Elsevier, vol. 43(2), pages 329-334, December.
    26. Timothy L. Sorenson, 2004. "Limit Pricing with Incomplete Information: Answers to Frequently Asked Questions," The Journal of Economic Education, Taylor & Francis Journals, vol. 35(1), pages 62-78, January.
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    Cited by:

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    3. Colucci, Domenico & Doni, Nicola & Ricchiuti, Giorgio & Valori, Vincenzo, 2022. "Market dynamics with a state-owned dominant firm and a competitive fringe," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Miguel Ángel Ropero, 2021. "Entry deterrence when the potential entrant is your competitor in a different market," Southern Economic Journal, John Wiley & Sons, vol. 87(3), pages 1010-1030, January.
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    6. Semmler, Willi & Di Bartolomeo, Giovanni & Minooei Fard, Behnaz & Braga, Joao Paulo, 2022. "Limit pricing and entry game of renewable energy firms into the energy sector," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 179-190.
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    More about this item

    Keywords

    Dynamic limit pricing; Dynamic signaling; Entry deterrence;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices

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