How to use a strategic game to optimize the performance of CDMA wireless network synchronization

The purpose of this chapter is to illustrate some possible applications of non-cooperative game theory to the issue of resource allocation in a multi-user CDMA wireless system, as a typical example of a licensed infrastructure network. To this aim, the first part of the chapter revisits some fundamental results of non-cooperative game theory, by means of some toy examples taken from practical problems in the context of wireless communications. In particular, we introduce the notion of games with strict incomplete information, which have a relevant application in many decentralized algorithms, owing to their inherent robustness and adaptiveness. The approach considered here is based upon the concept of energy efficiency, which aims at finding a tradeoff between obtaining good performance and saving as much energy as possible for both classes of terminals. This interplay can be captured by formulating the problem as a non-cooperative generalized Nash game with strict incomplete information, that combines the tools of a non-cooperative game-theoretic formulation together with some key concepts from algorithmic mechanism design. The solution of the game is expedient to derive an iterative and distributed algorithm that enables each terminal to locally regulate its optimal transmit power without any knowledge about the operating status of all others. The improvement provided by the proposed approach is evaluated in a practical context by means of a numerical example.