Roy Chowdhury, Prabal (2007): BertrandEdgeworth equilibrium with a large number of firms.

PDF
MPRA_paper_3353.pdf Download (367kB)  Preview 
Abstract
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 gridunit 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 tiebreaking rule is `weakly manipulable'.
Item Type:  MPRA Paper 

Institution:  Indian Statistical Institute, Delhi Center 
Original Title:  BertrandEdgeworth equilibrium with a large number of firms 
Language:  English 
Keywords:  Bertrand equilibrium; Edgeworth paradox; tiebreaking rule; rationing rule; folk theorem of perfect competition 
Subjects:  D  Microeconomics > D4  Market Structure, Pricing, and Design > D41  Perfect Competition D  Microeconomics > D4  Market Structure, Pricing, and Design > D43  Oligopoly and Other Forms of Market Imperfection L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets 
Item ID:  3353 
Depositing User:  Prabal Roy Chowdhury 
Date Deposited:  30. May 2007 
Last Modified:  16. Feb 2013 23:37 
References:  Allen, B. and M. Hellwig, 1986, BertrandEdgeworth oligopoly in large markets, Review of Economic Studies 53, 175204. Allen, B. and M. Hellwig, 1993, BertrandEdgeworth duopoly with proportional residual demand, International Economic Review 34, 3960. Borgers, T., 1992, Iterated elimination of dominated strategies in a BertrandEdgeworth model, Review of Economic Studies 59, 163176. Chamberlin, E.H., 1933, The Theory of Monopolistic Competition (Cambridge: Harvard University Press). Davidson, C. and R. Deneckere, 1986, Long run competition in capacity, short run competition in price, and the Cournot model, RAND Journal of Economics 17, 404415. Deneckere, R.J. and D. Kovenock, 1996, BertrandEdgeworth duopoly with unit cost asymmetry, Economic Theory 8, 125. Dixon, H., 1984, The existence of mixedstrategy equilibria in a pricesetting oligopoly with convex costs, Economics Letters 16, 205212. Dixon, H., 1987, Approximate Bertrand equilibria in a replicated industry, Review of Economic Studies 54, 4762. Dixon, H., 1990, BertrandEdgeworth equilibria when firms avoid turning customers away, Journal of Industrial Economics 39, 131146. Dixon, H., 1993, Integer pricing and BertrandEdgeworth oligopoly with strictly convex costs: Is it worth more than a penny? Bulletin of Economic Research 45, 257268. Edgeworth, F., 1897, La teoria pura del monopolio, Giornale Degli Economisti 40, 1331. Fudenberg, D. and J. Tirole, 1987, Understanding rentdissipation: On the use of game theory in industrial organization, American Economic Review 77, 176183. Gale, D. and H. Nikaido, 1965, The Jacobian matrix and the global univalence of mapping, Mathematische Annalen 159, 8193. Harrington, J., 1989, A reevaluation of perfect competition as the solution to the Bertrand price game, Mathematical Social Sciences 17, 315328. Kreps, D.M. and J.A. Scheinkman, 1983, Quantity precommitment and Bertrand competition yield Cournot outcomes, Bell Journal of Economics 14, 326337. Levitan, R. and M. Shubik, 1972, Price duopoly and capacity constraints, International Economic Review 13, 111122. Maskin, E., 1986, The existence of equilibrium with pricesetting firms, American Economic Review 76, 382386. Maskin, E. and J. Tirole, 1988, A theory of dynamic oligopoly II: Price competition, kinked demand curves, and Edgeworth cycles, Econometrica 56, 571599. Novshek, W., 1980, Cournot equilibrium with free entry, Review of Economic Studies 67, 473486. Novshek, W. and P. Roy Chowdhury, 2003, Bertrand equilibria with entry: Limit results, International Journal of Industrial Organization 21, 795808. Novshek, W. and H. Sonnenschein, 1983, Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies, Journal of Economic Theory 30, 171187. Osborne, M.J. and C. Pitchik, 1986, Price competition in a capacityconstrained duopoly, Journal of Economic Theory 38, 238260. Ray Chaudhuri, P., 1996, The contestable outcome as a Bertrand equilibrium, Economics Letters 50, 237242. Roy Chowdhury, P., 1999, BertrandEdgeworth equilibria with unobservable output, uncoordinated consumers and large number of firms, Economics Letters 63, 207211. Ruffin, R.J., 1971, Cournot oligopoly and competitive behavior, Review of Economic Studies 38, 493502. Shubik, M., 1959, Strategy and Market Structure (Wiley, New York). Tasnadi, A., 1999a, Existence of pure strategy Nash equilibrium in BertrandEdgeworth oligopolies, Economics Letters 63, 201206. Tasnadi, A., 1999b, A twostage BertrandEdgeworth game, Economics Letters 65, 353358. Tirole, J., 1988, The Theory of Industrial Organization (MIT Press, Cambridge). Vives, X., 1986, Rationing rules and BertrandEdgeworth equilibria in large markets, Economics Letters 21, 113116. Vives, X., 1999. Oligopoly Pricing: Old Ideas and New Tools (MIT Press). Yoshida, Y., 2002, BertrandEdgeworth price competition with strictly convex cost functions, Discussion paper No. 64, Department of Economics, Seikei University. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/3353 