Chapter 1 - A Very Short Tour of Game Theory

Abstract

This chapter focuses on wireless games. The meaning of a player can be very broad; it can be a human being, a machine, an automaton, an animal, and a plant. The purpose of the game theory is to model interactions between players, to define different types of possible outcome, to predict the solutions of a game under given information and behavior assumptions, to characterize all possible outcomes of the game, and to design good strategies to reach some of these outcomes. There are three main types of representation of a game: the normal or strategic form, the extensive form, and the coalitional form. There are some main features which distinguish games in different main classes: static and dynamic games, non-stochastic and stochastic games, non-cooperative and cooperative games, games with complete/incomplete information, games with perfect/imperfect information, and zero-sum games, and non zero-sum games. Further, this chapter concerns some fundamental notions of game theory, which are actions, pure strategies, and mixed strategies. The scope of this theory includes the concepts of rational decision-makers, selfish decision-makers, and non-cooperative games. The new concepts need to be invented and the theory enriched with new interaction models. This scenario seems likely to happen in the wireless community if game theory remains as a major paradigm for building modern communications systems.