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The Stackelberg Equilibria of the Kelly Mechanism

  • Francesco De PellegriniEmail author
  • Antonio Massaro
  • Tamer Başar
Conference paper
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

The Kelly mechanism dictates that players share a resource proportionally to their bids. The corresponding game is known to have a unique Nash equilibrium. A related question arises, which is the nature of the behavior of the players for different prices imposed by the resource owner, who may be viewed as the leader in a Stackelberg game where the other players are followers. In this work, we describe the dynamics of the Nash equilibrium as a function of the price. Toward that goal, we characterize analytical properties of the Nash equilibrium by means of the implicit function theorem. With regard to the revenue generated by the resource owner, we provide a counterexample which shows that the Stackelberg equilibrium of the Kelly mechanism may not be unique. We obtain sufficient conditions which guarantee the set of Stackelberg equilibria to be finite and unique in the symmetric case. Finally, we describe the dependency between the resource’s signal and the maximum revenue that the resource owner can generate.

Keywords

Kelly mechanism Nash equilibrium Stackelberg equilibrium 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Francesco De Pellegrini
    • 1
    • 2
    Email author
  • Antonio Massaro
    • 2
  • Tamer Başar
    • 3
  1. 1.CERI/LIAUniversity of AvignonAvignonFrance
  2. 2.Fondazione Bruno KesslerTrentoItaly
  3. 3.University of Illinois at Urbana ChampaignUrbanaUSA

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