英文：When Strategic Customers Meet Strategic Servers: Individual and Social Optimization in Many-Server Queueing Systems
中文题目：策略型顾客遇到策略型服务器：多服务台排队系统中的个体与社会优化
时间: 2026年3月7日（周六） 上午10点
主讲人: Amy R. Ward，University of Chicago
Bio:
Amy R. Ward is a Professor of Operations Management at the University of Chicago in the Booth School of Business. She received Ph.D. from Stanford in Management Science and Engineering in 2001. Amy Ward's research focuses on the approximation and control of stochastic systems, with applications to the service industry. Much of her past work has focused on the impact of customer impatience and abandonments on performance. Her more recent work investigates the interactions between behavioral incentives and operational efficiency in service systems. Ward is a fellow of the INFORMS Manufacturing and Service Operations Management (MSOM) Society, and is the Editor-in-Chief for the journal Operations Research. In the past, she was Editor-in-Chief for the journal Operations Research Letters, and earlier held the position of Chair of the Applied Probability Society.
照片：
Abstract:
We initiate the study of joint strategic behavior of customers and servers in many-server queueing systems. We model customers as strategic agents who decide whether to join the system by weighing reward from service against cost of waiting, following the seminal works of Naor (1969) and Knudsen (1972). In those works, customers use a threshold equilibrium joining strategy based on the number of customers already in the system. Moreover, customers "over-join" compared to the socially optimal threshold, a result known as Naor's inequality. Although Naor's inequality is known to hold widely in queueing systems with strategic customers, no work has considered whether or not it holds when servers are also strategic. We investigate this question within a large-system asymptotic framework when servers choose service rates to balance reward and effort cost. We show that at equilibrium, customers may either over-join or under-join the system, an observation that challenges the universality of Naor's inequality. Next, we compare the welfare of customers and servers under the social optimum and an individual equilibrium and find the following imbalance: While customers always benefit when moving from an equilibrium to the social optimum, servers may end up experiencing reduced and even negative utility. Finally, we propose an incentive scheme that charges an entry fee from customers and offers a performance-based compensation for servers, which realigns individual incentives with social optimum. The incentive scheme is feasible when the number of servers is sufficiently small. Surprisingly, under the optimal incentive scheme, the welfare distribution remains imbalanced but towards the opposite party: Servers always benefit, while customers sometimes incur welfare losses.