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Evolutionary coalitional games for random access control

  • SI: Analytical and Stochastic Modeling
  • Published:
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Abstract

This paper considers a random access system with several users and one shared medium. Each user has its own queue (of packets) which can be empty or not. We propose an evolving coalitional game between the users and analyze the system outcomes. Unlike classical coalitional approaches that assume that coalitional structures are fixed and formed cost-free, we explain how coalitions can be formed in a fully distributed manner using evolutionary dynamics and coalitional combined fully distributed payoff and strategy (CODIPAS) learning. We introduce the concept of evolutionarily stable coalitional structure (ESCS), which, when it is formed, is resilient to small perturbation of strategies. We show that (1) the formation and the stability of coalitions depend mainly on the cost of making a coalition compared to the benefit of cooperation, (2) the grand coalition can be unstable and a localized coalitional structure is formed as an evolutionarily stable coalitional structure. When the core is empty, the coalitional CODIPAS scheme selects one element of the stable set. Finally, we discuss the convergence and complexity of the proposed coalitional learning in access control with different users’ activities. Some extensions to cognitive medium access control with queue management are provided.

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Notes

  1. Note that one can use a proportional split of the surplus instead of equal split, i.e., \(\alpha \) fraction of the surplus goes to user 1 and \((1-\alpha ) \) fraction to user 2 for some \(\alpha \in (0,1).\)

  2. We do not consider an infinite population of users nor pairwise interactions.

  3. We are not aware of the convergence time of a learning procedure in the context of games in coalitional form (such as the classical split-and-merge procedure) in dynamical network formation.

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Acknowledgments

This work is partially supported by the NYU Global Seed Grants for Collaborative Research program. We would like to thank the Editor and three anonymous reviewers for their constructive comments, which helped us to improve the manuscript. This work has been started when the authors were with Ecole Superieure d’Electricite, Supelec, France. Part of this work was the Master Thesis of Miss Xin Luo under the supervision of Hamidou Tembine. We are grateful to the conference participants at ASMTA 2012 Analytical and Stochastic Modelling Techniques and Applications for their valuable comments and suggestions on the preliminary version of the present work. Short version of this work appeared in the proceedings of INFOCOM 2013, Torino, Italy, Luo and Tembine (2013).

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  1. Xin Luo

    Present address: Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

  2. Hamidou Tembine

    Present address: Learning and Game Theory Lab, New York University Abu Dhabi, Abu Dhabi, UAE

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    1. Xin Luo
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    2. Hamidou Tembine
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    Correspondence to Hamidou Tembine.

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    Luo, X., Tembine, H. Evolutionary coalitional games for random access control. Ann Oper Res (2016). https://doi.org/10.1007/s10479-016-2198-0

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