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Selfish Routing in Capacitated Networks

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  • Correa, Jose R.
  • Schulz, Andreas S.
  • Stier Moses, Nicolas E.

Abstract

According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e. the system optimum. In this paper, we offer extensions of recent positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable and even discontinuous. The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hithert

Suggested Citation

  • Correa, Jose R. & Schulz, Andreas S. & Stier Moses, Nicolas E., 2003. "Selfish Routing in Capacitated Networks," Working papers 4319-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:3533
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    File URL: http://hdl.handle.net/1721.1/3533
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    References listed on IDEAS

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    Cited by:

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    3. José R. Correa & Nicolás Figueroa & Nicolás E. Stier-Moses, 2008. "Pricing with markups in industries with increasing marginal costs," Documentos de Trabajo 256, Centro de Economía Aplicada, Universidad de Chile.
    4. Karakostas, George & Kim, Taeyon & Viglas, Anastasios & Xia, Hao, 2011. "On the degradation of performance for traffic networks with oblivious users," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 364-371, February.
    5. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    6. Feng, Zengzhe & Gao, Ziyou & Sun, Huijun, 2014. "Bounding the inefficiency of atomic splittable selfish traffic equilibria with elastic demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 63(C), pages 31-43.
    7. Roughgarden, Tim & Schoppmann, Florian, 2015. "Local smoothness and the price of anarchy in splittable congestion games," Journal of Economic Theory, Elsevier, vol. 156(C), pages 317-342.
    8. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. 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.
    10. 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.
    11. 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.

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