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Bertrand-Edgeworth equilibrium with a large number of firms

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  • Prabal Roy Chowdhury

    (Indian Statistical Institute, New Delhi)

Abstract

We examine a model of price competition where the firms simultaneously decide on both price and quantity, and are free to supply less than the quantity demanded. We demonstrate that if the tie-breaking rule is `non-manipulable', then, for a large class of rationing rules, there is a unique equilibrium in pure strategies whenever the number of firms is large enough. We then show that the `folk theorem' of perfect competition holds. Finally, we examine if the results go through when the firms are asymmetric, or produce to order.

Suggested Citation

  • Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Discussion Papers 04-12, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:04-12
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    References listed on IDEAS

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    1. Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-1172, September.
    2. R. J. Ruffin, 1971. "Cournot Oligopoly and Competitive Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 493-502.
    3. 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.
    4. 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.
    5. 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.
    6. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    7. 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 571-599, May.
    8. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    9. Dubey, Pradeep, 1982. "Price-Quantity Strategic Market Games," Econometrica, Econometric Society, vol. 50(1), pages 111-126, January.
    10. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    11. Huw Dixon, 1987. "Approximate Bertrand Equilibria in a Replicated Industry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 47-62.
    12. 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 257-268, July.
    13. 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.
    14. 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.
    15. 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.
    16. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    17. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    18. Dixon, Huw, 1990. "Bertrand-Edgeworth Equilibria when Firms Avoid Turning Customers Away," Journal of Industrial Economics, Wiley Blackwell, vol. 39(2), pages 131-146, December.
    19. William Novshek, 1980. "Cournot Equilibrium with Free Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 473-486.
    20. Simon, Leo K., 1987. "Bertrand price competition with differentiated commodities," Journal of Economic Theory, Elsevier, vol. 41(2), pages 304-332, April.
    21. Prabal Roy Chowdhury, 2002. "Limit-pricing as Bertrand equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 811-822.
    22. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    23. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
    24. 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.
    25. James W. Friedman, 1988. "On the Strategic Importance of Prices versus Quantities," RAND Journal of Economics, The RAND Corporation, vol. 19(4), pages 607-622, Winter.
    26. 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 301-309, March.
    27. Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-386, May.
    28. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    29. Tilman Börgers, 1992. "Iterated Elimination of Dominated Strategies in a Bertrand-Edgeworth Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 163-176.
    30. 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 111-122, February.
    31. 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.
    32. 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.
    33. Mandy, David M, 1992. "Nonuniform Bertrand Competition," Econometrica, Econometric Society, vol. 60(6), pages 1293-1330, November.
    34. Leo K. Simon, 1984. "Bertrand, the Cournot Paradigm and the Theory of Perfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 209-230.
    35. 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.
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    More about this item

    Keywords

    Bertrand equilibrium; pure strategy; non-manipulable tiebreaking rule;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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