Pricing equilibrium of transportation systems with behavioral commuters

Lien Jaimie W.; Mazalov Vladimir V.; Zheng Jie

doi:10.3934/jdg.2020026

Article Contents

2020, Volume 7, Issue 4: 335-350. Doi: 10.3934/jdg.2020026

This issue Previous Article Real option value and poverty trap Next Article Behavior-based pricing in service differentiated industries

Pricing equilibrium of transportation systems with behavioral commuters

1.
Department of Decision Sciences and Managerial Economics, CUHK Business School, Chinese University of Hong Kong, Hong Kong SAR, China
2.
Saint-Petersburg State University, St. Petersburg, Russia, Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, Russia
3.
Department of Economics, School of Economics and Management, Tsinghua University, Beijing, China, 100084

^* Corresponding author: Vladimir V. Mazalov
^* Corresponding author: Vladimir V. Mazalov

Received: March 31, 2020

Early access: August 2020

Published: October 2020

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Abstract

We study Wardrop equilibrium in a transportation system with profit-maximizing firms and heterogeneous commuters. Standard commuters minimize the sum of monetary costs and equilibrium travel time in their route choice, while "oblivious" commuters choose the route with minimal idle time. Three possible scenarios can arise in equilibrium: A pooling scenario where all commuters make the same transport choice; A separating scenario where different types of commuters make different transport choices; A partial pooling scenario where some standard commuters make the same transport choice as the oblivious commuters. We characterize the equilibrium existence condition, derive equilibrium flows, prices and firms' profits in each scenario, and conduct comparative analyses on parameters representing route conditions and heterogeneity of commuters, respectively. The framework nests the standard model in which all commuters are standard as a special case, and also allows for the case in which all commuters are oblivious as the other extreme. Our study shows how the presence of behavioral commuters under different route conditions affects equilibrium behavior of commuters and firms, as well a the equilibrium outcome of the transportation system.

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Mathematics Subject Classification: Primary: 90B20, 91A10; Secondary: 91B42.

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Figure 1. 2-Route Transportation System with Duopoly Firms and Heterogeneous Commuters

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Figure 2. The regions of optimal behavior of commuters and firms

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