Bertrand-Edgeworth equilibrium with a large number of firms
We examine a model of price competition with strictly convex costs where the firms simultaneously decide on both price and quantity, are free to supply less than the quantity demanded, and there is discrete pricing. If firms are symmetric then, for a large class of residual demand functions, there is a unique equilibrium in pure strategies whenever, for a fixed grid size, the number of firms is sufficiently large. Moreover, this equilibrium price is within a grid-unit of the competitive price. The results go through to a large extent when the firms are asymmetric, or they are symmetric but play a two-stage game and the tie-breaking rule is 'weakly manipulable'.
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- 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.
- Osborne, Martin J. & Pitchik, Carolyn, 1983. "Price Competition in a Capacity-Constrained Duopoly," Working Papers 83-08, C.V. Starr Center for Applied Economics, New York University.
- Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
- Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer, vol. 8(1), pages 1-25.
- Prabal Roy Chowdhury, 2002. "Limit-pricing as Bertrand equilibrium," Economic Theory, Springer, vol. 19(4), pages 811-822.
- Simon, Leo K., 1987. "Bertrand price competition with differentiated commodities," Journal of Economic Theory, Elsevier, vol. 41(2), pages 304-332, April.
- Chowdhury, Prabal Roy, 1999. "Bertrand-Edgeworth equilibria with unobservable output, uncoordinated consumers and large number of firms," Economics Letters, Elsevier, vol. 63(2), pages 207-211, May.
- Mestelman, Stuart & Welland, Deborah & Welland, Douglas, 1987. "Advance production in posted offer markets," Journal of Economic Behavior & Organization, Elsevier, vol. 8(2), pages 249-264, June.
- repec:oup:restud:v:53:y:1986:i:1:p:1-26 is not listed on IDEAS
- Tasnadi, Attila, 1999. "Existence of pure strategy Nash equilibrium in Bertrand-Edgeworth oligopolies," Economics Letters, Elsevier, vol. 63(2), pages 201-206, May.
- repec:oup:restud:v:38:y:1971:i:116:p:493-502 is not listed on IDEAS
- Dixon, Huw David, 1992. "The Competitive Outcome as the Equilibrium in an Edgeworthian Price-Quantity Model," Economic Journal, Royal Economic Society, vol. 102(411), pages 301-09, March.
- Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
- repec:oup:restud:v:53:y:1986:i:2:p:175-204 is not listed on IDEAS
- David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
- Levitan, Richard & Shubik, Martin, 1972.
"Price Duopoly and Capacity Constraints,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February.
- Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
- repec:oup:restud:v:51:y:1984:i:2:p:209-30 is not listed on IDEAS
- repec:oup:restud:v:47:y:1980:i:3:p:473-86 is not listed on IDEAS
- Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium: Manipulable residual demand," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 04-15, Indian Statistical Institute, New Delhi, India.
- Tasnadi, Attila, 1999. "A two-stage Bertrand-Edgeworth game," Economics Letters, Elsevier, vol. 65(3), pages 353-358, December.
- Fudenberg, Drew & Tirole, Jean, 1987. "Understanding Rent Dissipation: On the Use of Game Theory in Industrial Organization," American Economic Review, American Economic Association, vol. 77(2), pages 176-83, May.
- Dubey, Pradeep, 1982.
"Price-Quantity Strategic Market Games,"
Econometric Society, vol. 50(1), pages 111-26, January.
- Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
- Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-86, May.
- Allen, Beth & Hellwig, Martin, 1993. "Bertrand-Edgeworth Duopoly with Proportional Residual Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 39-60, February.
- Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-72, September.
- Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
- repec:oup:restud:v:54:y:1987:i:1:p:47-62 is not listed on IDEAS
- repec:oup:restud:v:53:y:1986:i:1:p:27-41 is not listed on IDEAS
- repec:oup:restud:v:59:y:1992:i:1:p:163-76 is not listed on IDEAS
- Dixon, Huw, 1984. "The existence of mixed-strategy equilibria in a price-setting oligopoly with convex costs," Economics Letters, Elsevier, vol. 16(3-4), pages 205-212.
- Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, June.
- Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
- Dixon, Huw David, 1993. "Integer Pricing and Bertrand-Edgeworth Oligopoly with Strictly Convex Costs: Is It Worth More Than a Penny?," Bulletin of Economic Research, Wiley Blackwell, vol. 45(3), pages 257-68, July.
- Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May.
- Dixon, Huw, 1990. "Bertrand-Edgeworth Equilibria when Firms Avoid Turning Customers Away," Journal of Industrial Economics, Wiley Blackwell, vol. 39(2), pages 131-46, December.
- Mandy, David M, 1992. "Nonuniform Bertrand Competition," Econometrica, Econometric Society, vol. 60(6), pages 1293-30, November.
- Novshek, William & Chowdhury, Prabal Roy, 2003. "Bertrand equilibria with entry: limit results," International Journal of Industrial Organization, Elsevier, vol. 21(6), pages 795-808, June.
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