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Evolutionary Games for Multiple Access Control

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 12))

Abstract

In this paper, we formulate an evolutionary multiple access control game with continuous-variable actions and coupled constraints. We characterize equilibria of the game and show that the pure equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specific equilibrium solution using the concepts of normalized equilibrium and evolutionarily stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics, such as Brown–von Neumann–Nash dynamics, Smith dynamics, and replicator dynamics. In addition, we examine correlated equilibrium for the single-receiver model. Correlated strategies are based on signaling structures before making decisions on rates. We then focus on evolutionary games for hybrid additive white Gaussian noise multiple-access channel with multiple users and multiple receivers, where each user chooses a rate and splits it over the receivers. Users have coupled constraints determined by the capacity regions. Building upon the static game, we formulate a system of hybrid evolutionary game dynamics using G-function dynamics and Smith dynamics on rate control and channel selection, respectively. We show that the evolving game has an equilibrium and illustrate these dynamics with numerical examples.

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Notes

  1. 1.

    † This material is based upon work supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) under grant number FA9550-09-1-0249, and in part by the AFOSR MURI Grant FA9550-10-1-0573.The material in this paper was partially presented in [9] and [10].

  2. 2.

    Note that the set of constrained strong equilibria is a subset of the set of NEs (by taking coalitions of size one) and any constrained strong equilibrium is Pareto optimal (by taking coalition of full size).

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Author information

Authors and Affiliations

  1. Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1308 W. Main Street, Urbana, IL, 61801, USA

    Quanyan Zhu & Hamidou Tembine

  2. Department of Telecommunications, École Supérieure d’Electricité (SUPELEC), 3 rue Joliot-Curie, 91192, Gif-Sur-Yvette Cedex, France

    Tamer Başar

Authors
  1. Quanyan Zhu
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  2. Hamidou Tembine
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  3. Tamer Başar
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Correspondence to Quanyan Zhu .

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Editors and Affiliations

  1. , CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Pierre Cardaliaguet

  2. Wilfrid Laurier University, University Ave W 75, Waterloo, N2L 3C5, Ontario, Canada

    Ross Cressman

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Zhu, Q., Tembine, H., Başar, T. (2013). Evolutionary Games for Multiple Access Control. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_3

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