Algorithmic Aspects of Discrete Choice in Convex Optimization

verfasst von: David Müller

Verlag: Springer Fachmedien Wiesbaden

Buchreihe : Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis

Über dieses Buch

This book develops a framework to analyze algorithmic aspects of discrete choice models in convex optimization. The central aspect is to derive new prox-functions from discrete choice surplus functions, which are then incorporated into convex optimization schemes. The book provides further economic applications of discrete choice prox-functions within the context of convex optimization such as network manipulation based on alternating minimization and dynamic pricing for online marketplaces.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The role of discrete choice models in convex optimization is discussed. Classically, discrete choice models describe a decision-making problem in an economic context (McFadden, 1978). Since then, a countless amount of researchers applied these models to identify choice-affecting characteristics or attributes. As well, a lot of research papers were devoted to the development of new discrete choice models. A good overview of existing literature can be found in Anderson et al. (1992) or Train (2009).

David Müller

Chapter 2. Discrete Choice Models

Abstract

Discrete choice models enjoy a broad popularity in the research community as well as amongst practitioners in the industry. From a theoretical point of view these models attract researchers of different fields due to their interdisciplinary character. Central aspect is the analysis of individual choices, since discrete choice models analyze how and why decisions are made.

David Müller

Chapter 3. Discrete Choice Prox-Functions

Abstract

We analyze the duality relation between random utility models and representative agent models, which has already been mentioned in Sect. 2.2. We derive new prox-functions on the simplex from additive random utility models and semi-parametric choice models. More precisely, the convex conjugate of the surplus function of certain discrete choice models satisfies the properties of prox-functions, known from optimization.

David Müller

Chapter 4. Consumption Cycle

Abstract

We illustrate the benefit of discrete choice prox-functions derived in Chapter 3 in an economic framework. Therefore, we focus on the question of consumer’s utility maximization. More particularly, discrete choice prox-functions are applied for the adjustment of consumer’s demand.

David Müller

Chapter 5. Network Manipulation

Abstract

In this chapter we present another application of discrete choice prox-functions. In fact, we elaborate a network manipulation algorithm based on an alternating minimization scheme from Nesterov (2020). In our context, the alternative process mimics the natural behavior of agents and organizations operating on a network.

David Müller

Chapter 6. Dynamic Pricing

Abstract

Recently, there is growing interest and need for dynamic pricing algorithms, especially, in the field of online marketplaces by offering smart pricing options for big online stores. The dynamic adjustment of prices attracts researchers and practitioners from different areas, such as economics, operations research, computer science and econometrics. Therefore, the amount of existing literature concerning dynamic pricing is extensive.

David Müller

Chapter 7. Conclusion and Perspectives

Abstract

This text presents several ways to incorporate discrete choice models into convex optimization schemes. The analysis is motivated by problems of computational economics, such as e. g. consumption behavior, diffusion of information, and dynamic pricing. As the foundation, we study the strong convexity of the convex conjugate of the surplus functions due to different discrete choice models.

David Müller

Backmatter

Titel: Algorithmic Aspects of Discrete Choice in Convex Optimization
verfasst von: David Müller
Verlag: Springer Fachmedien Wiesbaden
Electronic ISBN: 978-3-658-45705-1
Print ISBN: 978-3-658-45704-4
DOI: https://doi.org/10.1007/978-3-658-45705-1