Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T05:03:28.969Z Has data issue: false hasContentIssue false
  • English
  • Français

The potentially negative effects of cooperation in service systems

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  29 April 2020

Hakjin Chung ,
Hyun-Soo Ahn  and
Rhonda Righter
Hakjin Chung*
Affiliation:
Korea Advanced Institute of Science and Technology
Hyun-Soo Ahn*
Affiliation:
University of Michigan
Rhonda Righter*
Affiliation:
University of California, Berkeley
*
*Postal address: KAIST College of Business, Seoul, 02455, Republic of Korea. Email address: hakjin.chung@kaist.ac.kr
**Postal address: Ross School of Business, University of Michigan, Ann Arbor, MI 48109, USA. Email address: hsahn@umich.edu
***Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: rrighter@ieor.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The ‘Price of Anarchy’ states that the performance of multi-agent service systems degrades with the agents’ selfishness (anarchy). We investigate a service model in which both customers and the firm are strategic. We find that, for a Stackelberg game in which the server invests in capacity before customers decide whether or not to join, there can be a ‘Benefit of Anarchy’, that is, customers acting selfishly can have a greater overall utility than customers who are coordinated to maximize their overall utility. We also show that customer anarchy can be socially beneficial, resulting in a ‘Social Benefit of Anarchy’. We show that such phenomena are rather general and can arise in multiple settings (e.g. in both profit-maximizing and welfare-maximizing firms, in both capacity-setting and price-setting firms, and in both observable and unobservable queues). However, the underlying mechanism leading to the Benefit of Anarchy can differ significantly from one setting to another.

Keywords

QueueingPrice of Anarchybalkingindividual versus social welfare

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K25: Queueing theory
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 1 , March 2020 , pp. 319 - 347
Copyright
© Applied Probability Trust 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Borgs, C., Chayes, J. T., Doroudi, S., Harchol-Balter, M. andXu, K. (2014). The optimal admission threshold in observable queues with state dependent pricing. Prob. Eng. Inf. Sci. 28, 101–119.CrossRefGoogle Scholar
Chen, H. andFrank, M. (2004). Monopoly pricing when customers queue. IIE Trans. 36, 569–581.CrossRefGoogle Scholar
De Vany, A. (1976). Uncertainty, waiting time, and capacity utilization: a stochastic theory of product quality. J. Political Econom. 84 (3), 523–541.CrossRefGoogle Scholar
Dewan, S. andMendelson, H. (1990). User delay costs and internal pricing for a service facility. Manag. Sci. 36, 1502–1517.CrossRefGoogle Scholar
Edelson, N. M. andHilderbrand, D. K. (1975). Congestion tolls for Poisson queuing processes. Econometrica 43, 81–92.CrossRefGoogle Scholar
Gilboa-Freedman, G., Hassin, R. andKerner, Y. (2014). The Price of Anarchy in the Markovian single server queue. IEEE Trans. Automatic Control 59, 455–459.CrossRefGoogle Scholar
Grassmann, W. K. (1979). The economic service rate. J. Operat. Res. Soc. 30, 149–155.CrossRefGoogle Scholar
Hassin, R. (1986). Consumer information in markets with random product quality: the case of queues and balking. Econometrica 54, 1185–1195.CrossRefGoogle Scholar
Hassin, R. (2016). Rational Queueing. CRC press.CrossRefGoogle Scholar
Hassin, R. andHaviv, M. (2003). To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer Science and Business Media.CrossRefGoogle Scholar
Haviv, M. andRoughgarden, T. (2007). The Price of Anarchy in an exponential multi-server. Operat. Res. Lett. 35, 421–426.CrossRefGoogle Scholar
Knudsen, N. C. (1972). Individual and social optimization in a multiserver queue with a general cost-benefit structure. Econometrica 40, 515–528.CrossRefGoogle Scholar
Lippman, S. A. andStidham, S. Jr (1977). Individual versus social optimization in exponential congestion systems. Operat. Res. 25, 233–247.CrossRefGoogle Scholar
Littlechild, S. (1974). Optimal arrival rate in a simple queueing system. Internat. J. Production Research 12, 391–397.CrossRefGoogle Scholar
Maxey, T., Chung, H., Ahn, H.-S. andRighter, R. (2017). When is anarchy beneficial? ACM SIGMETRICS Performance Evaluation Review 45, 18–20.CrossRefGoogle Scholar
Mendelson, H. (1985). Pricing computer services: queueing effects. Commun. Assoc. Comput. Mach. 28, 312–321.Google Scholar
Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica 37, 15–24.CrossRefGoogle Scholar
Roughgarden, T. (2005). Selfish Routing and the Price of Anarchy. MIT Press, Cambridge, MA.Google Scholar
Stidham, S. Jr (1992). Pricing and capacity decisions for a service facility: stability and multiple local optima. Manag. Sci. 38, 1121–1139.CrossRefGoogle Scholar
Yechiali, U. (1971). On optimal balking rules and toll charges in the GI/M/1 queuing process. Operat. Res. 19, 349–370.CrossRefGoogle Scholar
Yechiali, U. (1972). Customers’ optimal joining rules for the GI/M/s queue. Manag. Sci. 18, 434–443.CrossRefGoogle Scholar
Zhang, J., Pourazarm, S., Cassandras, C. G. andPaschalidis, I. C. (2018). The Price of Anarchy in transportation networks: data-driven evaluation and reduction strategies. Proc. IEEE 106, 538–553.CrossRefGoogle Scholar