Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed-Logit Demand

• 成果类型: Article
• 署名作者: Morrow, W. Ross; Skerlos, Steven J.
• 署名单位: Iowa State University; University of Michigan System; University of Michigan
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1100.0894
• 发表日期: 2011
• 页码: 328-345
• 关键词: differentiated products; FUEL EFFICIENCY; krylov methods; MARKET; COMPETITION; models; STANDARDS; systems; CHOICE

摘要

This article describes numerical methods that exploit fixed-point equations equivalent to the first-order condition for Bertrand-Nash equilibrium prices in a class of differentiated product market models based on the mixed-logit model of demand. One fixed-point equation is already prevalent in the literature, and one is novel. Equilibrium prices are computed for the calendar year 2005 new-vehicle market under two mixed-logit models using (i) a state-of-the-art variant of Newton's method applied to the first-order conditions as well as the two fixed-point equations and (ii) a fixed-point iteration generated by our novel fixed-point equation. A comparison of the performance of these methods for a simple model with multiple equilibria is also provided. The analysis and trials illustrate the importance of using fixed-point forms of the first-order conditions for efficient and reliable computations of equilibrium prices.