Ex-post price stability with convex costs

Martin Byford

International Journal of Game Theory, 2018, vol. 47, issue 4, No 2, 1065-1085

Abstract: 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.

Keywords: Bertrand competition; Cournot competition; Convex costs; Non-transferable utility coalitional games; Core convergence; Double-marginalisation (search for similar items in EconPapers)
JEL-codes: C71 D43 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-017-0599-1

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