A hierarchical network game with a large number of players

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We consider a hierarchical network game with multiple links, a single service provider, and a large number of users with multiple classes, where different classes of users enter the network and exit it at different nodes. Each user is charged by the service provider a fixed price per unit of bandwidth used on each link in its route, and chooses the level of its flow by maximizing an objective function that shows a trade-off between the disutility of the payment to the service provider and congestion cost on the link the user uses, and the utility of its flow. The service provider, on the other hand, wishes to maximize the total revenue it collects. We formulate this problem as a leader-follower (Stackelberg) game, with a single leader (the service provider, who sets the price) and a large number of Nash followers (the users, who decide on their flow rates). We show that the game admits a unique equilibrium, and obtain the solution in analytic form. A detailed study of the limiting case where the number of followers is large reveals a number of interesting and intuitive properties of the equilibrium, and answers the question of whether and when the service provider has the incentive to add additional capacity to the network in response to an increase in the number of users on a particular link.

Original languageEnglish (US)
Pages (from-to)373-378
Number of pages6
JournalIFAC Proceedings Volumes (IFAC-PapersOnline)
Issue number1
StatePublished - Jan 1 2002
Event15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain
Duration: Jul 21 2002Jul 26 2002


  • Communication networks
  • Equilibrium
  • Game theory
  • Nash games
  • Stackelberg games

ASJC Scopus subject areas

  • Control and Systems Engineering


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