  This article presents a detailed technical framework for modeling with
Bertrand-Nash equilibrium prices under Mixed Logit demand. Two coercive
fixed-point equations provide more stable computational methods than those
obtained from the literal first-order conditions. Assumptions to justify
derivation and use of these equations are provided. A brief discussion of a
GMRES-Newton method with hookstep globalization strategy originally due to
Viswanath is also given. This article can be considered a supplement to an
article by the authors forthcoming in the journal {\em Operations Research}.
