Strategic equilibrium versus global optimum for a pair of competing servers

Benjamin Avi-Itzhak, Boaz Golany, Uriel G. Rothblum

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1165-1172
Number of pages8
JournalJournal of Applied Probability
Volume43
Issue number4
DOIs
StatePublished - Dec 2006

Keywords

  • Linear reward scheme
  • Nash equilibrium
  • Queueing system

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty

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