Queueing Systems

, Volume 76, Issue 3, pp 243–265 | Cite as

Modeling a case of herding behavior in a multi-player game

  • Guy FayolleEmail author
  • Jean-Marc Lasgouttes


The system mentioned in the title belongs to the family of the so-called massively multi-player online social games. It features a scoring system for the elements of the game that is prone to herding effects. We analyze in detail its stationary regime in the thermodynamic limit, when the number of players tends to infinity. In particular, for some classes of input sequences and selection policies, we provide necessary and sufficient conditions for the existence of a complete meanfield-like measure, showing off an interesting condensation phenomenon.


Thermodynamical limit Condensation Ergodicity Transience Non-linear differential system Banach space 

Mathematics Subject Classification

60J28 34L30 37C40 



This work was supported by Grant 109-2167/R from the Région Île-de-France.


  1. 1.
    Cartan, H.: Cours de calcul différentiel. Collection Méthodes. Hermann, Paris (1997)Google Scholar
  2. 2.
    Delcoigne, F., Fayolle, G.: Thermodynamical limit and propagation of chaos in polling systems. Markov Process. Relat. Fields 5(1), 89–124 (1999)Google Scholar
  3. 3.
    Ethier, S.N., Kurtz, T.G.: Markov Processes Characterization and Convergence Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Wiley, New York (1986)Google Scholar
  4. 4.
    Fuchs, B.A., Levin, V.I.: Functions of a Complex Variable and Some of Their Applications, vol. II. Pergamon Press, London (Translated by J. Berry; edited by T. Kövari) (1961)Google Scholar
  5. 5.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 7th edn. Academic Press, New York (2007)Google Scholar
  6. 6.
    Ince, E.L.: Ordinary Differential Equations. Dover Publications, New York (1956)Google Scholar
  7. 7.
    Ma Micro Planète., (2011). (in French) Accessed 21 May 2013
  8. 8.
    Titchmarsh, E.C.: The Theory of Function, 2nd edn. Oxford University Press, Oxford (1939)Google Scholar
  9. 9.
    Veeraraghavan, S., Debo, L.: Joining longer queues: information externalities in queue choice. Manuf. Serv. Oper. Manag. 11, 543–562 (2009)Google Scholar
  10. 10.
    Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: A queueing system with a choice of the shorter of two queues–an asymptotic approach. Probl. Peredachi Inform. 32(1), 20–34 (1996)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.INRIA Paris–RocquencourtLe Chesnay cedexFrance

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