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Stackelberg thresholds in network routing games or the value of altruism

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  • Sharma, Yogeshwer
  • Williamson, David P.

Abstract

It is well known that the Nash equilibrium in network routing games can have strictly higher cost than the optimum cost. In Stackelberg routing games, where a fraction of flow is centrally-controlled, a natural problem is to route the centrally-controlled flow such that the overall cost of the resulting equilibrium is minimized. We consider the scenario where the network administrator wants to know the minimum amount of centrally-controlled flow such that the cost of the resulting equilibrium solution is strictly less than the cost of the Nash equilibrium. We call this threshold the Stackelberg threshold and prove that for networks of parallel links with linear latency functions, it is equal to the minimum of the Nash flows on links carrying more optimum flow than Nash flow. Our approach also provides a simpler proof of characterization of the minimum fraction that must be centrally controlled to induce the optimum solution.

Suggested Citation

  • Sharma, Yogeshwer & Williamson, David P., 2009. "Stackelberg thresholds in network routing games or the value of altruism," Games and Economic Behavior, Elsevier, vol. 67(1), pages 174-190, September.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:174-190
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    References listed on IDEAS

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    1. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
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    Cited by:

    1. Richárd Kicsiny, 2017. "Solution for a class of closed-loop leader-follower games with convexity conditions on the payoffs," Annals of Operations Research, Springer, vol. 253(1), pages 405-429, June.
    2. Kicsiny, R. & Varga, Z. & Scarelli, A., 2014. "Backward induction algorithm for a class of closed-loop Stackelberg games," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1021-1036.

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