Bertrand Equilibria and Sharing Rules
We analyse how sharing rules affect Nash equilibria in Bertrand games, where the sharing of profits at ties is a decisive assumption. Necessary conditions for either positive or zero equilibrium profits are derived. Zero profit equilibria are shown to exist under weak conditions if the sharing rule is ‘sign-preserving’. For Bertrand markets we define the class of ‘expectation sharing rules’, where profits at ties are derived from some distribution of quantities. In this class the winner-takes-all sharing rule is the only one that is always sign-preserving, while for each pair of demand and cost functions there may be many others.
|Date of creation:||Mar 2005|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 44 - 20 - 7183 8801
Fax: 44 - 20 - 7183 8820
|Order Information:|| Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hoernig, Steffen H., 2002. "Mixed Bertrand equilibria under decreasing returns to scale: an embarrassment of riches," Economics Letters, Elsevier, vol. 74(3), pages 359-362, February.
- Leo K. Simon and William R. Zame., 1987.
"Discontinuous Games and Endogenous Sharing Rules,"
Economics Working Papers
8756, University of California at Berkeley.
- Todd R. Kaplan & David Wettstein, 2000. "The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition," Spanish Economic Review, Springer, vol. 2(1), pages 65-71.
- John Morgan & Michael R. Baye, 2002. "Winner-take-all price competition," Economic Theory, Springer, vol. 19(2), pages 271-282.
- Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
- Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Harrington, Joseph Jr., 1989. "A re-evaluation of perfect competition as the solution to the Bertrand price game," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 315-328, June.
- Osborne, Martin J. & Pitchik, Carolyn, 1983.
"Price Competition in a Capacity-Constrained Duopoly,"
83-08, C.V. Starr Center for Applied Economics, New York University.
- Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
- Sharkey, William W. & Sibley, David S., 1993. "A Bertrand model of pricing and entry," Economics Letters, Elsevier, vol. 41(2), pages 199-206.
- Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
- Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:4972. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()The email address of this maintainer does not seem to be valid anymore. Please ask to update the entry or send us the correct address
If references are entirely missing, you can add them using this form.