In-Queue Priority Purchase: A Dynamic Game Approach

45 Pages Posted: 12 Sep 2018 Last revised: 8 Sep 2020

See all articles by Zhongbin Wang

Zhongbin Wang

Nankai University - Business School

Luyi Yang

University of California, Berkeley - Haas School of Business

Shiliang Cui

Georgetown University - McDonough School of Business

Jinting Wang

Beijing Jiaotong University; Central University of Finance and Economics

Date Written: August 31, 2018

Abstract

Pay-for-priority is a common practice in congestion-prone service systems. In many applications, customers are allowed to pay and upgrade to priority at any time of their stay in the queue, even if they choose not to do so initially. However, this dynamic in-queue priority-purchasing behavior of strategic customers has been unexplored in the extant literature, which, instead, assumes that the only epoch to purchase priority is upon arrival, and if customers choose not to upgrade, they cannot do so later during their wait. To fill this gap, we build a queueing-game-theoretic model in this paper that explicitly captures customers’ in-queue priority-purchasing behavior. We show that under the assumption that all customers (who have not upgraded yet) simultaneously decide whether to upgrade, 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, under the sequential upgrade rule, pure-strategy equilibria may exist, which we confirm analytically in a small buffer system and in a general buffer system with sufficiently light or heavy traffic, and numerically in a system that can hold at most three customers. Regardless of the rule in use, in-queue priority purchase yields less revenue than upon-arrival priority purchase in a small buffer system.

Keywords: In-queue decision, Dynamic game, Priority purchase, Upgrade, Strategic 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). Available at SSRN: https://ssrn.com/abstract=3242430 or http://dx.doi.org/10.2139/ssrn.3242430

Zhongbin Wang

Nankai University - Business School ( email )

Baidi Road
Tianjin, 300071
China

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 )

Washington, DC 20057
United States

Jinting Wang

Beijing Jiaotong University ( email )

No.3 of Shangyuan Residence Haidian District
Beijing, 100089
China

Central University of Finance and Economics ( email )

Beijing, Beijing 100081
China

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