Logit需求下Bertrand-Nash均衡价格的存在性
On the Existence of Bertrand-Nash Equilibrium Prices Under Logit Demand
摘要：
本文提出了一个证明的存在性的Bertrand-Nash均衡价格与多产品的企业和Logit模型的需求，不依赖于限制性假设的产品特性，企业的同质性或对称性，产品成本，或线性的效用函数。证明是基于间接效用函数的条件，从一阶条件导出的不动点方程，以及对二阶条件的直接分析，从而导致利润最大化价格的唯一性。随后的几个结果也表明，Logit需求模型下的价格均衡不能充分描述多产品定价。
英文摘要：
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.
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