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A geometric approach to the price of anarchy in nonatomic congestion games

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  • Correa, José R.
  • Schulz, Andreas S.
  • Stier-Moses, Nicolás E.

Abstract

We present a short, geometric proof for the price-of-anarchy results that have recently been established in a series of papers on selfish routing in multicommodity flow networks and on nonatomic congestion games. This novel proof also facilitates two new types of theoretical results: On the one hand, we give pseudo-approximation results that depend on the class of allowable cost functions. On the other hand, we derive stronger bounds on the inefficiency of equilibria for situations in which the equilibrium costs are within reasonable limits of the fixed costs. These tighter bounds help to explain empirical observations in vehicular traffic networks. Our analysis holds in the more general context of nonatomic congestion games, which provide the framework in which we describe this work.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:457-469
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    References listed on IDEAS

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    1. A. de Palma & Y. Nesterov, 1997. "Optimization formulations and static equilibrium in congested transportation networks," THEMA Working Papers 97-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Patrice Marcotte & Sang Nguyen & Alexandre Schoeb, 2004. "A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks," Operations Research, INFORMS, vol. 52(2), pages 191-212, April.
    3. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    5. 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.
    6. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2007. "Fast, Fair, and Efficient Flows in Networks," Operations Research, INFORMS, vol. 55(2), pages 215-225, April.
    7. 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.
    8. 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.
    9. Milchtaich, Igal, 2004. "Social optimality and cooperation in nonatomic congestion games," Journal of Economic Theory, Elsevier, vol. 114(1), pages 56-87, January.
    10. Igal Milchtaich, 2000. "Generic Uniqueness of Equilibrium in Large Crowding Games," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 349-364, August.
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