The Stackelberg Equilibria of the Kelly Mechanism

Francesco De Pellegrini, Antonio Massaro, M Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationStatic and Dynamic Game Theory
Subtitle of host publicationFoundations and Applications
PublisherBirkhauser
Pages107-123
Number of pages17
DOIs
StatePublished - Jan 1 2019

Publication series

NameStatic and Dynamic Game Theory: Foundations and Applications
ISSN (Print)2363-8516
ISSN (Electronic)2363-8524

Fingerprint

Stackelberg Equilibrium
Resources
Nash Equilibrium
Stackelberg Game
Implicit Function Theorem
Counterexample
Stackelberg equilibrium
Game
Sufficient Conditions
Owners
Nash equilibrium

Keywords

  • Kelly mechanism
  • Nash equilibrium
  • Stackelberg equilibrium

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability
  • Applied Mathematics

Cite this

De Pellegrini, F., Massaro, A., & Basar, M. T. (2019). The Stackelberg Equilibria of the Kelly Mechanism. In Static and Dynamic Game Theory: Foundations and Applications (pp. 107-123). (Static and Dynamic Game Theory: Foundations and Applications). Birkhauser. https://doi.org/10.1007/978-3-030-10880-9_7

The Stackelberg Equilibria of the Kelly Mechanism. / De Pellegrini, Francesco; Massaro, Antonio; Basar, M Tamer.

Static and Dynamic Game Theory: Foundations and Applications. Birkhauser, 2019. p. 107-123 (Static and Dynamic Game Theory: Foundations and Applications).

Research output: Chapter in Book/Report/Conference proceedingChapter

De Pellegrini, F, Massaro, A & Basar, MT 2019, The Stackelberg Equilibria of the Kelly Mechanism. in Static and Dynamic Game Theory: Foundations and Applications. Static and Dynamic Game Theory: Foundations and Applications, Birkhauser, pp. 107-123. https://doi.org/10.1007/978-3-030-10880-9_7
De Pellegrini F, Massaro A, Basar MT. The Stackelberg Equilibria of the Kelly Mechanism. In Static and Dynamic Game Theory: Foundations and Applications. Birkhauser. 2019. p. 107-123. (Static and Dynamic Game Theory: Foundations and Applications). https://doi.org/10.1007/978-3-030-10880-9_7
De Pellegrini, Francesco ; Massaro, Antonio ; Basar, M Tamer. / The Stackelberg Equilibria of the Kelly Mechanism. Static and Dynamic Game Theory: Foundations and Applications. Birkhauser, 2019. pp. 107-123 (Static and Dynamic Game Theory: Foundations and Applications).
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