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

Autor:	Morrow, W. Ross, Skerlos, Steven J.
Rok vydání:	2010
Předmět:	Quantitative Finance - General Finance Computer Science - Computer Science and Game Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 39 Pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1012.5832 Zobrazit plný text záznamu View this record from Arxiv