Abstract
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.
Original language | English |
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Pages (from-to) | 1165-1172 |
Number of pages | 8 |
Journal | Journal of Applied Probability |
Volume | 43 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2006 |
Keywords
- Linear reward scheme
- Nash equilibrium
- Queueing system
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty