# Stability in price competition revisited

Research Article

First Online:

- 88 Downloads

## Abstract

We consider consumers with the same reservation price, who desire to buy at most one unit of a good. Firms compete only in prices, but there are other features firms cannot control that would eventually lead an agent to buy in one firm or another. We introduce such uncertainty in a model of a price competition game with incomplete information. This competition takes place under stability and we provide equilibrium existence results. We analyze different specifications of residual demands which yield further interpretations that deepen the phenomenon of price dispersion, Bertrand’s paradox and market power.

## Keywords

Price competition Incomplete information Nash equilibrium Approximate equilibrium Price dispersion## JEL Classification

D4 L13 L00 L1 C70## References

- Balder, E.J.: Generalized equilibrium results for games with incomplete information. Math. Oper. Res.
**13**, 265–276 (1988)CrossRefGoogle Scholar - Balder, E.J.: An equilibrium existence result for games with incomplete information and indeterminate outcomes. J. Math. Econ.
**40**, 297–320 (2004)CrossRefGoogle Scholar - Bagwell, K., Lee, G.: Number of firms and price competition. Working-Paper (2014)Google Scholar
- Carbonell-Nicolau, O., McLean, R.P.: On the existence of Nash equilibrium in Bayesian games. Working Paper. Rutgers University (2014)Google Scholar
- Chamberlin, E.: The Theory of Monopolistic Competition. Harvard University Press, Cambridge (1933)Google Scholar
- Chamberlin, E.: Monopolistic imperfect competition? Q. J. Econ.
**51**, 557–580 (1937)CrossRefGoogle Scholar - He, W., Yannelis, N.C.: Discontinuous games with asymmetric information: an extension of Reny’s existence theorem. Games Econ. Behav.
**91**, 26–35 (2015a)CrossRefGoogle Scholar - He, W., Yannelis, N.C.: Existence of equilibria in discontinuous Bayesian games. Working-Paper (2015b)Google Scholar
- Hotelling, H.: Stability in competition. Econ. J.
**39**, 41–57 (1929)CrossRefGoogle Scholar - Kaldor, N.: Market imperfection and excess capacity. Economica
**2**, 33–50 (1935)CrossRefGoogle Scholar - Milgrom, P., Weber, R.: Distributional strategies for games with incomplete information. Math. Oper. Res.
**10**, 619–632 (1985)CrossRefGoogle Scholar - Okun, A.M.: Prices and Quantities: A Macroeconomic Analysis. The Brookings Institution, Washington, D.C. (1981)Google Scholar
- Reny, P.J.: On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica
**67**, 1029–1056 (1999)CrossRefGoogle Scholar - Salop, S., Stiglitz, J.: Bargains and ripoffs: a model of monopolistically competitive price dispersion. Rev. Econ. Stud.
**44**, 493–510 (1977)CrossRefGoogle Scholar - Spulber, D.F.: Bertrand competition when rivals’ costs are unknown. J. Ind. Econ.
**43**(1), 1–11 (1995)CrossRefGoogle Scholar - Varian, H.R.: A model of sales. Am. Econ. Rev.
**70**, 651–659 (1980)Google Scholar

## Copyright information

© Society for the Advancement of Economic Theory 2015