Dynamic Games and Applications

, Volume 3, Issue 1, pp 3–23 | Cite as

Stochastic Differential Games and Energy-Efficient Power Control

  • François MériauxEmail author
  • Samson Lasaulce
  • Hamidou Tembine


One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The players are the transmitters who adapt their power level to the quality of their time-varying link with the receiver, their battery level, and the strategy updates of the others. The proposed model not only allows one to take into account long-term strategic interactions, but also long-term energy constraints. A simple sufficient condition for the existence of a Nash equilibrium in this game is provided and shown to be verified in a typical scenario. As the uniqueness and determination of equilibria are difficult issues in general, especially when the number of players goes large, we move to two special cases: the single player case which gives us some useful insights of practical interest and allows one to make connections with the case of large number of players. The latter case is treated with a mean-field game approach for which reasonable sufficient conditions for convergence and uniqueness are provided. Remarkably, this recent approach for large system analysis shows how scalability can be dealt with in large games and only relies on the individual state information assumption.


Differential games Energy efficiency Mean-field games Power control Wireless networks 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • François Mériaux
    • 1
    Email author
  • Samson Lasaulce
    • 1
  • Hamidou Tembine
    • 2
  1. 1.Laboratoire des Signaux et SystèmesGif sur YvetteFrance
  2. 2.Department of TelecommunicationsÉcole Supérieure d’Électricité (SUPELEC)Gif sur YvetteFrance

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