Roy Chowdhury, Prabal (2007): Bertrand-Edgeworth equilibrium with a large number of firms.
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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'.
|Item Type:||MPRA Paper|
|Institution:||Indian Statistical Institute, Delhi Center|
|Original Title:||Bertrand-Edgeworth equilibrium with a large number of firms|
|Keywords:||Bertrand equilibrium; Edgeworth paradox; tie-breaking rule; rationing rule; folk theorem of perfect competition|
|Subjects:||D - Microeconomics > D4 - Market Structure and Pricing > D41 - Perfect Competition
D - Microeconomics > D4 - Market Structure and Pricing > 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
|Depositing User:||Prabal Roy Chowdhury|
|Date Deposited:||30. May 2007|
|Last Modified:||16. Feb 2013 23:37|
Allen, B. and M. Hellwig, 1986, Bertrand-Edgeworth oligopoly in large markets, Review of Economic Studies 53, 175-204.
Allen, B. and M. Hellwig, 1993, Bertrand-Edgeworth duopoly with proportional residual demand, International Economic Review 34, 39-60.
Borgers, T., 1992, Iterated elimination of dominated strategies in a Bertrand-Edgeworth model, Review of Economic Studies 59, 163-176.
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, 404-415.
Deneckere, R.J. and D. Kovenock, 1996, Bertrand-Edgeworth duopoly with unit cost asymmetry, Economic Theory 8, 1-25.
Dixon, H., 1984, The existence of mixed-strategy equilibria in a price-setting oligopoly with convex costs, Economics Letters 16, 205-212.
Dixon, H., 1987, Approximate Bertrand equilibria in a replicated industry, Review of Economic Studies 54, 47-62.
Dixon, H., 1990, Bertrand-Edgeworth equilibria when firms avoid turning customers away, Journal of Industrial Economics 39, 131-146.
Dixon, H., 1993, Integer pricing and Bertrand-Edgeworth oligopoly with strictly convex costs: Is it worth more than a penny? Bulletin of Economic Research 45, 257-268.
Edgeworth, F., 1897, La teoria pura del monopolio, Giornale Degli Economisti 40, 13-31.
Fudenberg, D. and J. Tirole, 1987, Understanding rent-dissipation: On the use of game theory in industrial organization, American Economic Review 77, 176-183.
Gale, D. and H. Nikaido, 1965, The Jacobian matrix and the global univalence of mapping, Mathematische Annalen 159, 81-93.
Harrington, J., 1989, A reevaluation of perfect competition as the solution to the Bertrand price game, Mathematical Social Sciences 17, 315-328.
Kreps, D.M. and J.A. Scheinkman, 1983, Quantity precommitment and Bertrand competition yield Cournot outcomes, Bell Journal of Economics 14, 326-337.
Levitan, R. and M. Shubik, 1972, Price duopoly and capacity constraints, International Economic Review 13, 111-122.
Maskin, E., 1986, The existence of equilibrium with price-setting firms, American Economic Review 76, 382-386.
Maskin, E. and J. Tirole, 1988, A theory of dynamic oligopoly II: Price competition, kinked demand curves, and Edgeworth cycles, Econometrica 56, 571-599.
Novshek, W., 1980, Cournot equilibrium with free entry, Review of Economic Studies 67, 473-486.
Novshek, W. and P. Roy Chowdhury, 2003, Bertrand equilibria with entry: Limit results, International Journal of Industrial Organization 21, 795-808.
Novshek, W. and H. Sonnenschein, 1983, Walrasian equilibria as limits of non-cooperative equilibria. Part II: Pure strategies, Journal of Economic Theory 30, 171-187.
Osborne, M.J. and C. Pitchik, 1986, Price competition in a capacity-constrained duopoly, Journal of Economic Theory 38, 238-260.
Ray Chaudhuri, P., 1996, The contestable outcome as a Bertrand equilibrium, Economics Letters 50, 237-242.
Roy Chowdhury, P., 1999, Bertrand-Edgeworth equilibria with unobservable output, uncoordinated consumers and large number of firms, Economics Letters 63, 207-211.
Ruffin, R.J., 1971, Cournot oligopoly and competitive behavior, Review of Economic Studies 38, 493-502.
Shubik, M., 1959, Strategy and Market Structure (Wiley, New York).
Tasnadi, A., 1999a, Existence of pure strategy Nash equilibrium in Bertrand-Edgeworth oligopolies, Economics Letters 63, 201-206.
Tasnadi, A., 1999b, A two-stage Bertrand-Edgeworth game, Economics Letters 65, 353-358.
Tirole, J., 1988, The Theory of Industrial Organization (MIT Press, Cambridge).
Vives, X., 1986, Rationing rules and Bertrand-Edgeworth equilibria in large markets, Economics Letters 21, 113-116.
Vives, X., 1999. Oligopoly Pricing: Old Ideas and New Tools (MIT Press).
Yoshida, Y., 2002, Bertrand-Edgeworth price competition with strictly convex cost functions, Discussion paper No. 64, Department of Economics, Seikei University.