Stochastic Differential Games and Energy-Efficient Power Control
Fran\c{c}ois M\'eriaux, Samson Lasaulce, Hamidou Tembine (E3S)

TL;DR
This paper models energy-efficient power control in multi-user channels as a stochastic differential game, analyzing Nash equilibria and applying mean-field game theory for large systems to ensure scalability and practical insights.
Contribution
It formulates a stochastic differential game for power control considering long-term energy constraints and develops a mean-field approach for large systems.
Findings
Existence of Nash equilibrium under certain conditions.
Mean-field game approach ensures scalability in large systems.
Insights into single-player and multi-player interactions.
Abstract
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…
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