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Pathwise smooth splittable congestion games and inefficiency

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  • Raimondo, Roberto

Abstract

Very recently the inefficiency of Nash equilibria has been analyzed in the context of SplittableCongestionGames. These games are like the congestion games but allow the players to use convex combinations of subsets of resources. A new notion has been introduced in order to give bounds on the inefficiency or Price of Anarchy; such a notion has been termed the local smoothness. We present a unified framework where local smoothness and smoothness, a previously introduced notion, are presented as particular cases of a more general approach which we term pathwise smoothness. Such an approach is based partially on the Hadamard’s Lemma, which shows that it is possible to present any function, linear or not, by means of families of linear functions.

Suggested Citation

  • Raimondo, Roberto, 2020. "Pathwise smooth splittable congestion games and inefficiency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 15-23.
    • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:15-23
    DOI: 10.1016/j.jmateco.2019.10.006
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Pradeep Dubey, 1986. "Inefficiency of Nash Equilibria," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 1-8, February.
    4. Roberto Cominetti & José R. Correa & Nicolás E. Stier-Moses, 2009. "The Impact of Oligopolistic Competition in Networks," Operations Research, INFORMS, vol. 57(6), pages 1421-1437, 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. Blume, Lawrence & Easley, David & Kleinberg, Jon & Kleinberg, Robert & Tardos, Éva, 2015. "Introduction to computer science and economic theory," Journal of Economic Theory, Elsevier, vol. 156(C), pages 1-13.
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