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Dynamic Limit Pricing

  • Toxvaerd, Flavio

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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8104.

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Date of creation: Nov 2010
Date of revision:
Handle: RePEc:cpr:ceprdp:8104
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  1. Greg LeBlanc, 1992. "Signalling Strength: Limit Pricing and Predatory Pricing," RAND Journal of Economics, The RAND Corporation, vol. 23(4), pages 493-506, Winter.
  2. Loretta J. Mester, 1992. "Perpetual Signalling with Imperfectly Correlated Costs," RAND Journal of Economics, The RAND Corporation, vol. 23(4), pages 548-563, Winter.
  3. Grossman, Sanford J. & Perry, Motty, 1986. "Sequential bargaining under asymmetric information," Journal of Economic Theory, Elsevier, vol. 39(1), pages 120-154, June.
  4. Noldeke, Georg & van Damme, Eric, 1990. "Signalling in a Dynamic Labour Market," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 1-23, January.
  5. Kenneth L. Judd & Bruce C. Petersen, 1984. "Dynamic Limit Pricing and Internal Finance," Discussion Papers 603S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. Georg Nöldeke & Eric van Damme, 1990. "Switching Away From Probability One Beliefs," Discussion Paper Serie A 304, University of Bonn, Germany.
  8. Baron, David P, 1973. "Limit Pricing, Potential Entry, and Barriers to Entry," American Economic Review, American Economic Association, vol. 63(4), pages 666-74, September.
  9. 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.
  10. 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.
  11. Paul Milgrom & John Roberts, 1998. "Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis," Levine's Working Paper Archive 245, David K. Levine.
  12. Rubinstein, Ariel, 1985. "A Bargaining Model with Incomplete Information about Time Preferences," Econometrica, Econometric Society, vol. 53(5), pages 1151-72, September.
  13. 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.
  14. 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 981-96, July.
  15. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, June.
  16. Lippman, Steven A, 1980. "Optimal Pricing to Retard Entry," Review of Economic Studies, Wiley Blackwell, vol. 47(4), pages 723-31, July.
  17. De Bondt, Raymond R, 1976. "Limit Pricing, Uncertain Entry, and the Entry Lag," Econometrica, Econometric Society, vol. 44(5), pages 939-46, September.
  18. 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.
  19. Kaya, Ayça, 2009. "Repeated signaling games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 841-854, July.
  20. Weiss, Andrew, 1983. "A Sorting-cum-Learning Model of Education," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 420-42, June.
  21. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  22. Cho, In-Koo, 1990. "Uncertainty and Delay in Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 575-95, October.
  23. 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 275-93, May.
  24. 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.
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