On the Existence of Bertrand-Nash Equilibrium Prices Under Logit Demand
AbstractThis 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1012.5832.
Date of creation: Dec 2010
Date of revision: Jan 2012
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Web page: http://arxiv.org/
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