The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Todd R. Kaplan; David Wettstein

doi:10.1007/s101080050018

The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.

Original language	English
Pages (from-to)	65-71
Number of pages	7
Journal	Spanish Economic Review
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/s101080050018
State	Published - 1 Apr 2000
Externally published	Yes

Bibliographical note

Funding Information:
We wish to thank two referees and a co-editor for valuable suggestions that have significantly improved this paper. We also gratefully acknowledge the support from the Kreitman Foundation and the Monaster Center for Economic Research. This paper is a revised version of Kaplan and Wettstein [1997]. 1 See Shapiro (1989) for an exellent exposition of the two competing models.

Publisher Copyright:
© 2000, Springer-Verlag Berlin Heidelberg.

Keywords

JEL classification: C72, L13
Key words:Bertrand, price competition

ASJC Scopus subject areas

Economics, Econometrics and Finance (all)

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10.1007/s101080050018

Cite this

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abstract = "Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.",

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N2 - Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.

AB - Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.

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The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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