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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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    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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