Pricing in heterogeneous wireless networks

Hierarchical games and dynamics

Luca Rose, E. Veronica Belmega, Walid Saad, Merouane Debbah

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper, a novel game-theoretic model of the complex interactions between network service providers (NSPs) and users in heterogeneous small-cell networks is investigated. In this game, the NSPs selfishly aim at maximizing their profit while, simultaneously, the users seek to optimize their chosen service's quality-price tradeoff. A Stackelberg formulation in which the NSPs act as leaders and the users as followers is proposed. The users' interactions are modeled as a general nonatomic game. The existence of a Wardrop equilibrium (WE) in the users' game is proven, and its expression as a solution of a fixed-point equation is provided (irrespective of the number of NSPs, services offered, pricing policies, and QoS functions). Moreover, a set of sufficient conditions that ensure the uniqueness of the WE is provided. Notably, the uniqueness of the equilibrium for the particular case of congestion games is shown. An algorithm approximating these equilibria is provided and its convergence to an ε-WE is proven. The existence of Nash equilibria for the leaders' game is shown and illustrated via numerical simulations.

Original languageEnglish
Article number6820798
Pages (from-to)4985-5001
Number of pages17
JournalIEEE Transactions on Wireless Communications
Volume13
Issue number9
DOIs
StatePublished - Sep 1 2014

Fingerprint

Heterogeneous Wireless Networks
Heterogeneous networks
Pricing
Wireless networks
Profitability
Quality of service
Game
Computer simulation
Costs
Uniqueness
Congestion Games
Fixed-point Equation
Service Quality
User Interaction
Nash Equilibrium
Profit
Trade-offs
Optimise
Numerical Simulation
Formulation

Keywords

  • game theory
  • nonatomic game
  • Small-cell networks
  • Stackelberg game
  • Wardrop equilibrium (WE).

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Applied Mathematics

Cite this

Pricing in heterogeneous wireless networks : Hierarchical games and dynamics. / Rose, Luca; Belmega, E. Veronica; Saad, Walid; Debbah, Merouane.

In: IEEE Transactions on Wireless Communications, Vol. 13, No. 9, 6820798, 01.09.2014, p. 4985-5001.

Research output: Contribution to journalArticle

Rose, Luca ; Belmega, E. Veronica ; Saad, Walid ; Debbah, Merouane. / Pricing in heterogeneous wireless networks : Hierarchical games and dynamics. In: IEEE Transactions on Wireless Communications. 2014 ; Vol. 13, No. 9. pp. 4985-5001.
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