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A Stackelberg Network Game with a Large Number of Followers

Author

Listed:
  • T. Başar

    (University of Illinois)

  • R. Srikant

    (University of Illinois)

Abstract

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 tradeoff 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.

Suggested Citation

  • T. Başar & R. Srikant, 2002. "A Stackelberg Network Game with a Large Number of Followers," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 479-490, December.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:3:d:10.1023_a:1021294828483
    DOI: 10.1023/A:1021294828483
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    Citations

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    Cited by:

    1. Mao, Ying & Wang, Liqing & Liu, Yang & Lu, Jianquan & Wang, Zhen, 2018. "Stabilization of evolutionary networked games with length-r information," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 442-451.
    2. Elias Vathias & Stathes Hadjiefthymiades, 2022. "A stock options metaphor for content delivery networks," Netnomics, Springer, vol. 22(2), pages 195-230, October.
    3. Isabel Amigo & Pablo Belzarena & Sandrine Vaton, 2013. "A pricing scheme for QoS in overlay networks based on first-price auctions and reimbursement," Netnomics, Springer, vol. 14(1), pages 69-93, November.
    4. Chen, Ruoyun & Nozick, Linda, 2016. "Integrating congestion pricing and transit investment planning," Transportation Research Part A: Policy and Practice, Elsevier, vol. 89(C), pages 124-139.
    5. Panayides, Michalis & Knight, Vince & Harper, Paul, 2023. "A game theoretic model of the behavioural gaming that takes place at the EMS - ED interface," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1236-1258.
    6. Eduardo Mojica-Nava & Fredy Ruiz, 2021. "Stackelberg Population Dynamics: A Predictive-Sensitivity Approach," Games, MDPI, vol. 12(4), pages 1-15, November.
    7. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    8. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    9. Abay Molla Kassa & Semu Mitiku Kassa, 2017. "Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers," Journal of Global Optimization, Springer, vol. 68(4), pages 729-747, August.
    10. Elias Vathias & Stathes Hadjiefthymiades, 2021. "A stock options metaphor for content delivery networks," Netnomics, Springer, vol. 22(2), pages 195-230, December.
    11. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    12. Michael N. Vrahatis & Panagiotis Kontogiorgos & George P. Papavassilopoulos, 2020. "Particle Swarm Optimization for Computing Nash and Stackelberg Equilibria in Energy Markets," SN Operations Research Forum, Springer, vol. 1(3), pages 1-23, September.

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