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Strategic equilibrium versus global optimum for a pair of competing servers

Part of: Game theory Mathematical economics Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Benjamin Avi-Itzhak ,
Boaz Golany  and
Uriel G. Rothblum
Benjamin Avi-Itzhak*
Affiliation:
Rutgers University
Boaz Golany*
Affiliation:
Technion, Israel Institute of Technology
Uriel G. Rothblum*
Affiliation:
Technion, Israel Institute of Technology
*
∗Postal address: RUTCOR, Rutgers University, 640 Bartholomew Street, Piscataway, NJ 08854-8003, USA. Email address: aviitzha@rutcor.rutgers.edu
∗∗Postal address: Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, 32000, Israel.
∗∗Postal address: Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, 32000, Israel.
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Abstract

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Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

Keywords

Queueing systemNash equilibriumlinear reward scheme

MSC classification

Primary: 90B22: Queues and service
Secondary: 68M20: Performance evaluation; queueing; scheduling 91A05: 2-person games 91B52: Special types of equilibria
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1165 - 1172
Copyright
© Applied Probability Trust 2006 

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