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Ex-post price stability with convex costs

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  • Martin C. Byford

    (RMIT University)

Abstract

Homogeneous goods markets with convex costs, do not generally possess Bertrand-Nash equilibria in pure strategies. In order to identify ex-post stable prices in such markets, the set of outcomes feasible in Bertrand competition are analysed as a non-transferable utility coalitional game. The market-clearing price is shown to always implement a strict-core outcome. Moreover, where at least two sellers compete, the strict-core converges to only admit market-clearing outcomes. The analysis has implications for a number of prominent models of oligopoly competition. When firms engage in capacity pre-commitment, the set of ex-post stable prices converges to the corresponding Cournot prices. This result holds for arbitrary capacity choices and a general class of rationing rules. Conversely, double-marginalisation is never ex-post stable.

Suggested Citation

  • Martin C. Byford, 2018. "Ex-post price stability with convex costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1065-1085, November.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:4:d:10.1007_s00182-017-0599-1
    DOI: 10.1007/s00182-017-0599-1
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    References listed on IDEAS

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    1. Jonathan H. Hamilton & W. Bentley MacLeod & Jacques-François Thisse, 1991. "Spatial Competition and the Core," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 925-937.
    2. 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.
    3. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August.
    4. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1986. "Fairness and the Assumptions of Economics," The Journal of Business, University of Chicago Press, vol. 59(4), pages 285-300, October.
    5. 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.
    6. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard, 1986. "Fairness as a Constraint on Profit Seeking: Entitlements in the Market," American Economic Review, American Economic Association, vol. 76(4), pages 728-741, September.
    7. 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.
    8. Byford, Martin C., 2015. "A theoretical foundation for the undercut-proof equilibrium," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 209-220.
    9. Oz Shy, 1996. "Industrial Organization: Theory and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691795, December.
    10. Kujal, Praveen & Smith, Vernon L., 2008. "Fairness and Short Run Price Adjustment in Posted Offer Markets," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 6, pages 55-61, Elsevier.
    11. 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.
    12. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
    13. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    14. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    15. Mamoru Kaneko, 1976. "On the core and competitive equilibria of a market with indivisible goods," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 321-337, June.
    16. Daniel F. Spulber, 1986. "Second-Best Pricing and Cooperation," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 239-250, Summer.
    17. Harborne W. Stuart, Jr., 2005. "Biform Analysis of Inventory Competition," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 347-359, July.
    18. 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 competition; Cournot competition; Convex costs; Non-transferable utility coalitional games; Core convergence; Double-marginalisation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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