Methodologies for Analyzing Equilibria in Wireless Games

Publication Type:

Journal Article

Source:

IEEE Signal Processing Magazine, Special Issue on Game Theory for Signal Processing and Communication, Volume 26, Number 5, p.51-52 (2009)

Abstract:

nder certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where rational entities interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide nonexhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection, and efficiency. The major works by Von Neumann, Morgenstern, and Nash are recognized as real catalyzers for the theory of games, which originates from the works by Waldegrave (1713), Cournot (1838), Darwin (1871), Edgeworth (1881), Zermelo (1913), Borel (1921), and Ville (1938). Whereas the strong developments of game theory and information theory occured approximatively at the same time of history, (mainly in the middle of the 20th century with the major works by Von Neumann, Morgenstern, Nash, and Shannon), it is only recently that deepened analyses have been conducted, at a significant scale, to apply game theory to communications problems. During the 50 years following the seminal work by Shannon, only a small number of papers adopting a game-theoretic view of communication problems existed. To cite just a few of them, we have [1] where point-to-point communications are seen as a game between the channel encoder [choosing the best input distribution in terms of mutual information (MI)] and channel (choosing the worse transition probability in terms of MI); [2], where source coding is seen as a game between the source encoder and switcher (modifying the source distribution) having antagonistic objectives in terms of distorsion; [3] where the author exploits game theory for the joint signal-anddetector design using game-theoretic techniques to perform multiparameter optimization; and also [4], where a legal encoder-decoder pair fights against a jammer. By contrast, many papers exploiting game theory for communications and especially wireless communications have been released over the past 15 years (e.g., [5]–[9]) and the phenomenon seems to gain more and more momentum. There are many reasons for this craze for game theory in the wireless community, here we will give a few technical reasons for this. In this article, we will focus on technical problems arising at the physical and medium access layers of a wireless network, and not on economic aspects related to it, like the auction problem for spectrum, even though it is also an important scenario where game theory is used.

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