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Price of anarchy for non-atomic congestion games with stochastic demands

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  • Wang, Chenlan
  • Doan, Xuan Vinh
  • Chen, Bo

Abstract

We generalize the notions of user equilibrium, system optimum and price of anarchy to non-atomic congestion games with stochastic demands. In this generalized model, we extend the two bounding methods from Roughgarden and Tardos (2004) and Correa et al. (2008) to bound the price of anarchy, and compare the upper bounds we have obtained. Our results show that the price of anarchy depends not only on the class of cost functions but also demand distributions and, to some extent, the network topology. The upper bounds are tight in some special cases, including the case of deterministic demands.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:70:y:2014:i:c:p:90-111
    DOI: 10.1016/j.trb.2014.08.009
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    Cited by:

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    2. Macault, Emilien & Scarsini, Marco & Tomala, Tristan, 2022. "Social learning in nonatomic routing games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 221-233.
    3. 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.
    4. Rambha, Tarun & Boyles, Stephen D. & Unnikrishnan, Avinash & Stone, Peter, 2018. "Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 104-121.
    5. 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.
    6. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    7. Chenlan Wang & Xuan Vinh Doan & Bo Chen, 0. "Atomic congestion games with random players: network equilibrium and the price of anarchy," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.

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