In-Queue Priority Purchase: A Dynamic Game Approach

Queueing Systems, Forthcoming

41 Pages Posted: 12 Sep 2018 Last revised: 8 Feb 2023

See all articles by Zhongbin Wang

Zhongbin Wang

Tianjin University - College of Management and Economics

Luyi Yang

University of California, Berkeley - Haas School of Business

Shiliang Cui

Georgetown University - McDonough School of Business

Jinting Wang

Central University of Finance and Economics

Date Written: August 31, 2018

Abstract

Pay-for-priority is a common practice in congestion-prone service systems. The extant literature on this topic restricts attention to the case where the only epoch for customers to purchase priority is upon arrival, and if customers choose not to upgrade when they arrive, they cannot do so later during their wait. A natural alternative is to let customers pay and upgrade to priority at any time during their stay in the queue, even if they choose not to do so initially. This paper builds a queueing-game-theoretic model that explicitly captures self-interested customers' dynamic in-queue priority-purchasing behavior. When all customers (who have not upgraded yet) simultaneously decide whether to upgrade, we find in our model that pure-strategy equilibria do not exist under some intuitive criteria, contrasting the findings in classical models where customers can only purchase priority upon arrival. However, when customers sequentially decide whether to upgrade, threshold-type pure-strategy equilibria may exist. In particular, under sufficiently light traffic, if the number of ordinary customers accumulates to a certain threshold, then it is always the second last customer who upgrades, but in general, it could be a customer from another position and the queue-length threshold that triggers an upgrade can also vary with the traffic intensity. Finally, we find that in-queue priority purchase subject to the sequential rule yields less revenue than upon-arrival priority purchase in systems with small buffers.

Keywords: In-queue decision, Dynamic game, Priority upgrade, Self-interested customers

Suggested Citation

Wang, Zhongbin and Yang, Luyi and Cui, Shiliang and Wang, Jinting, In-Queue Priority Purchase: A Dynamic Game Approach (August 31, 2018). Queueing Systems, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3242430 or http://dx.doi.org/10.2139/ssrn.3242430

Zhongbin Wang

Tianjin University - College of Management and Economics ( email )

NO.92 Weijin Road
Nankai District
Tianjin, Tianjin 300072
China

HOME PAGE: http://come.tju.edu.cn/info/1092/5563.htm

Luyi Yang (Contact Author)

University of California, Berkeley - Haas School of Business ( email )

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States

Shiliang Cui

Georgetown University - McDonough School of Business ( email )

3700 O Street, NW
Washington, DC 20057
United States

Jinting Wang

Central University of Finance and Economics ( email )

Beijing, Beijing 100081
China

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