The supermarket game

Jiaming Xu, Bruce Hajek

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A supermarket game is considered with N FCFS queues with unit exponential service rate and global Poisson arrival rate Nλ. Upon arrival each customer chooses a number of queues to be sampled uniformly at random and joins the least loaded sampled queue. Customers are assumed to have cost for both waiting and sampling, and they want to minimize their own expected total cost. We study the supermarket game in a mean field model that corresponds to the limit as N converges to infinity in the sense that (i) for a fixed symmetric customer strategy, the joint equilibrium distribution of any fixed number of queues converges as N → ∞ to a product distribution determined by the mean field model and (ii) a Nash equilibrium for the mean field model is an e-Nash equilibrium for the finite N model with N sufficiently large. It is shown that there always exists a Nash equilibrium for λ < 1 and the Nash equilibrium is unique for λ 2 ≤ 1/2. Furthermore, we find that the action of sampling more queues by some customers has a positive externality on the other customers.

Original languageEnglish (US)
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Number of pages5
StatePublished - 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: Jul 1 2012Jul 6 2012

Publication series

NameIEEE International Symposium on Information Theory - Proceedings


Other2012 IEEE International Symposium on Information Theory, ISIT 2012
Country/TerritoryUnited States
CityCambridge, MA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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