The non-cooperative game theory applied to telecommunication systems

By Sara Riahi, Azzeddine Riahi

Abstract


In this paper, we outline various tools from the theory of non-cooperative games for studying competitive situations in telecommunication networks. We describe the mathematical tools while providing examples of various fields of telecommunication systems. In this paper, we study wireless systems in which mobile devices are autonomous in the choice of their communication configurations. This independence decision may involve, in particular the choice of the network access technology, the selection of the access point, the signal modulation, the frequency bands occupied, the power of the transmitted signal, etc. Typically, these configuration choices are made in order to maximize performance metrics specific to each terminal. Assuming that the terminals take their rational decisions to maximize their performance, game theory applies naturally to model the interactions between the decisions of different terminals. Specifically, the main objective of this article is to study emission power control equilibrium strategies to satisfy energy efficiency considerations. The framework of stochastic games is particularly suited to this problem and allows us in particular to characterize the region of performance achievable for all power control strategies that lead to a state of equilibrium. When the number of game terminals is large, we use the theory of mean field games to simplify the study of the system. This theory allows us to study not the individual interactions between the terminals, but the interaction of each terminal with an average field representing the overall state of the other terminals. Finally, for a power control game, the convergence of dynamics of better responses to equilibrium points has been studied.

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