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A note of network equilibrium and noncooperative games

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  • Devarajan, Shantayanan

Abstract

Rosenthal has shown that a user-optimized transportation network is equivalent to a pure Strategy Nash equilibrium when the network flows are discrete. Noting that most network equilibrium theorists take flows to be continuous, we extend this result to the nondiscrete case. We prove that a continuous flow, user-optimized network is a pure-strategy Nash equilibrium in a game with a continuum of pure strategies. Our "game", however, differs from Rosenthal's in its players, strategies, and payoffs. For instance, the players in our model are not the motorists, but the origin-destination pairs. Some possible applications and extensions of our results are discussed.

Suggested Citation

  • Devarajan, Shantayanan, 1981. "A note of network equilibrium and noncooperative games," Transportation Research Part B: Methodological, Elsevier, vol. 15(6), pages 421-426, December.
    • Handle: RePEc:eee:transb:v:15:y:1981:i:6:p:421-426
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    Cited by:

    1. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500068 is not listed on IDEAS
    2. Hugo E. Silva & Robin Lindsey & André de Palma & Vincent A. C. van den Berg, 2017. "On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users," Transportation Science, INFORMS, vol. 51(3), pages 863-881, August.
    3. Oran Richman & Nahum Shimkin, 2007. "Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 215-232, February.
    4. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    5. Wen-Long Jin, 2015. "Advances in Dynamic Traffic Assgmnt: TAC," Networks and Spatial Economics, Springer, vol. 15(3), pages 617-634, September.
    6. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
    7. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.

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