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Atomic congestion games with random players: network equilibrium and the price of anarchy

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  • Chenlan Wang

    (Beihang University)

  • Xuan Vinh Doan

    (University of Warwick)

  • Bo Chen

    (University of Warwick)

Abstract

In this paper, we present a new model of congestion games with finite and random number of players, and an analytical method to compute the random path and link flows. We study the equilibrium condition, reformulate it as an equivalent variational inequality problem, and establish the existence and non-uniqueness of the equilibria. We also upper bound the price of anarchy with affine cost functions to characterize the quality of the equilibria. The upper bound is tight in some special cases, including the case of deterministic players. Finally a general lower bound is also provided.

Suggested Citation

  • Chenlan Wang & Xuan Vinh Doan & Bo Chen, 2022. "Atomic congestion games with random players: network equilibrium and the price of anarchy," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2123-2142, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00583-3
    DOI: 10.1007/s10878-020-00583-3
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    References listed on IDEAS

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    1. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    2. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
    3. Correa, José & Hoeksma, Ruben & Schröder, Marc, 2019. "Network congestion games are robust to variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 69-78.
    4. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    5. Wang, Chenlan & Doan, Xuan Vinh & Chen, Bo, 2014. "Price of anarchy for non-atomic congestion games with stochastic demands," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 90-111.
    6. Correa, José R. & Schulz, Andreas S. & Stier-Moses, Nicolás E., 2008. "A geometric approach to the price of anarchy in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 457-469, November.
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