In order to relieve customers' waiting anxiety when queueing, many service providers provide waiting-area entertainment (WAE) by charging a service fee. This measure can effectively reduce customers' waiting cost and the queueing anxiety of them has been also greatly alleviated. By providing this option, it can not only attract more customers to join the system, but also add additional revenue to service providers. So it is widely favored. This paper establishes a queueing game model by focusing on the popular operation mode of “waiting-area entertainment” in the current service industry, and analyzes the impact of this option on the equilibrium behavior of customers and the revenue of service providers theoretically. The following results are derived in this paper. First, the Nash equilibrium joining strategy of customers is explored under observable and unobservable information cases. Second, the revenue-maximizing information disclosure strategy is derived, and it is optimal to reveal (conceal) queue length information to customers when market size is large (small). The revenue-maximizing service fee increases with the market size. Third, although WAE is provided an additional service option for releasing customers' anxiety for waiting, we find that when the market size is large, this option may hurt consumer surplus.
[1] Naor P. The regulation of queue size by levying tolls [J]. Econometrica, 1969, 37(1): 15-24.
[2] Edelson N M, Hilderbrand D K. Congestion tolls for Poisson queuing processes [J]. Econometrica, 1975, 43(1): 81-92.
[3] 张钰，王金亭.服务台不可靠的重试排队系统均衡分析[J].运筹学学报，2022，26(2)：1-15.
[4] 张淞钛，徐秀丽.具有两类故障特性的M/M/1排队系统均衡分析[J].运筹学学报，2019，23(4)： 131-142.
[5] 刘维奇，马琰，李继红.基于Geo/Geo/1(E，SV)排队系统的均衡止步策略[J].运筹学学报，2012, 16(2):65-76.
[6] Cui S, Wang Z, Yang L. The economics of line-sitting [J]. Management Science, 2020, 66(1): 227-242.
[7] Wang Z, Wang J. Pre-commitment or post-payment: Which worsens a line-sitting firm’s revenue? [J]. Operations Research Letters, 2019, 47(5): 447-451.
[8] Wang J, Cui S, Wang Z. Equilibrium strategies in M/M/1 priority queues with balking [J]. Production and Operations Management, 2019, 28(1): 43-62.
[9] Wang Z, Yang L, Cui S, et al. In-queue priority purchase: A dynamic game approach [J]. Queueing Systems, 2021, 97(3): 343-381.
[10] Gross D, Shortle J F, Thompson J M, et al. Fundamentals of Queueing Theory [M]. New Jersey: John Wiley & Sons, 2008.
[11] Hassin R, Haviv M. To Queue or not to Queue: Equilibrium Behavior in Queueing Systems [M]. Boston: Kluwer Academic Publishers, 2003.
[12] Hassin R. Rational Queueing [M]. Boca Raton: CRC Press, 2016.
[13] 王金亭.排队博弈论基础[M].北京：科学出版社，2016.
[14] 孙微，李世勇.经济学视角下的随机服务系统[M].北京：电子工业出版社，2017.
[15] Maister D H. The psychology of waiting lines [J]. Harvard Business School Background Note, 1985, 113-123.
[16] 王钟彬.基于“云排队”的经济效益分析[J].管理科学，2022，30(7):121-129.
[17] Yuan X, Dai T, Chen L G, et al. Co-opetition in service clusters with waiting-area entertainment [J]. Manufacturing & Service Operations Management, 2021, 23(1): 106-122.
[18] Li X, Lian Z, Shi Y. Capacity co-opetition in service clusters with waiting-area entertainment [EB/OL]. [2022-05-02]. http://dx.doi.org/10.2139/ssrn.3676177.
[19] 刘健，徐勇，印蓉蓉，等.基于顾客心理期望等待时间的服务策略研究[J].中国管理科学，2021， 29(2): 1-8.
[20] 刘健，徐勇，张珣，等，基于异质性顾客心理期望等待时间的优先权服务定价研究[J].中国管理科学，2022，30(1)：275-286.
[21] Chen H, Frank M. Monopoly pricing when customers queue [J]. IIE Transactions, 2004, 36(6): 569-581.
