Abstract
In this paper, we provide a result that shows existence and uniqueness of Nash equilibrium in cases in which existing methods are problematic. This result is based on a theorem by Kellogg (Proc Am Math Soc 60:207–210, 1976) that provides conditions for the existence of a unique fixed point. We apply it to the simple logit discrete choice model and the CES representative consumer model, where asymmetric cost firms produce multiple vertically and horizontally differentiated products and compete in prices.
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The authors thank Mark Armstrong, José Luis Moraga-González, Frank Verboven and anonymous referees for helpful remarks.
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Konovalov, A., Sándor, Z. On price equilibrium with multi-product firms. Econ Theory 44, 271–292 (2010). https://doi.org/10.1007/s00199-009-0486-5
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DOI: https://doi.org/10.1007/s00199-009-0486-5