Discrete choice prox-functions on the simplex

TL;DR

This paper introduces new convex prox-functions on the simplex derived from discrete choice models, providing probabilistic interpretations and applications in consumer demand adjustment within economic frameworks.

Contribution

It derives novel prox-functions from additive random utility models, including generalized extreme value and nested logit models, with explicit convexity parameters and applications.

Findings

Derived new convex prox-functions from discrete choice models.

Provided explicit convexity parameters for generalized extreme value models.

Applied the prox-functions to consumer demand adjustment in economic models.

Abstract

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to natural probabilistic interpretations of the iteration steps. As illustration we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming naturally adjusts demand within a consumption cycle.