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Topological Conditions for Uniqueness of Equilibrium in Networks

Author

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  • Igal Milchtaich

    () (Bar-Ilan University)

Abstract

Equilibrium flow in a physical network with a large number of users (e.g., transportation, communication, and computer networks) may not be unique if the costs of the network elements are not the same for all uses. Such differences among users may arise if they are not equally affected by congestion or have different intrinsic preferences. Whether or not, for all assignments of cost functions, each user’s equilibrium cost is the same in all Nash equilibria can be determined from the network topology. Specifically, this paper shows that in a two-terminal network, the equilibrium costs are always unique if and only if the network is one of several simple networks or consists of several such networks connected in series. The complementary class of all two-terminal networks with multiple equilibrium costs for some assignment of (user-specific) cost functions is similarly characterized by an embedded network of a particular simple type.

Suggested Citation

  • Igal Milchtaich, 2003. "Topological Conditions for Uniqueness of Equilibrium in Networks," Working Papers 2003-01, Bar-Ilan University, Department of Economics.
  • Handle: RePEc:biu:wpaper:2003-01
    as

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    File URL: http://www.biu.ac.il/soc/ec/wp/1-03/1-03.pdf
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, March.
    2. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Congestion; externalities; equilibrium flow; network topology; uniqueness of equilibrium.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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