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

W. Ross Morrow () and Steven J. Skerlos ()
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W. Ross Morrow: Departments of Mechanical Engineering and Economics, Iowa State University, Ames, Iowa 50014
Steven J. Skerlos: Department of Mechanical Engineering, University of Michigan, Ann Arhor, Michigan 48105

Operations Research, 2011, vol. 59, issue 2, 328-345

Abstract: 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.

Keywords: Bertrand-Nash equilibrium prices; differentiated product markets; mixed logit; Newton's method; GMRES-Newton hookstep; fixed-point iteration (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (20)

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