Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Product positioning under price competition
Management Science
Mathematical Programming: Series A and B
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Optimizing multinomial logit profit functions
Management Science
Matrix computations (3rd ed.)
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
On backtracking failure in newton-GMRES methods with a demonstration for the navier-stokes equations
Journal of Computational Physics
A Likelihood Approach to Estimating Market Equilibrium Models
Management Science
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
SIAM Journal on Numerical Analysis
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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.