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On the Existence of Bertrand-Nash Equilibrium Prices Under Logit Demand

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  • W. Ross Morrow
  • Steven J. Skerlos

Abstract

This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or symmetry, product costs, or linearity of the utility function. The proof is based on conditions for the indirect utility function, fixed-point equations derived from the first-order conditions, and a direct analysis of the second-order conditions resulting in the uniqueness of profit-maximizing prices. Several subsequent results also demonstrate that price equilibrium under the Logit model of demand cannot adequately describe multi-product pricing.

Suggested Citation

  • W. Ross Morrow & Steven J. Skerlos, 2010. "On the Existence of Bertrand-Nash Equilibrium Prices Under Logit Demand," Papers 1012.5832, arXiv.org, revised Jan 2012.
    • Handle: RePEc:arx:papers:1012.5832
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    References listed on IDEAS

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    1. Amil Petrin, 2002. "Quantifying the Benefits of New Products: The Case of the Minivan," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 705-729, August.
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    Cited by:

    1. W. Morrow, 2015. "Finite purchasing power and computations of Bertrand–Nash equilibrium prices," Computational Optimization and Applications, Springer, vol. 62(2), pages 477-515, November.

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