An Introduction to Game Theory

Abstract

This chapter presents introductory materials on game theory. It is written mainly for readers who have some basic mathematical background on algebra, probability and set theory but may or may not have any prior exposure to game theory. It summarizes the important concepts and definitions for readers to understand the content in the next few chapters, which are the main theme of this book—potential games. Unlike what most game-theoretic texts often do, we limit our theoretical exposition to only elemental concepts which are sufficient to comprehend the materials in this monograph. We focus on the discussion of strategic-form non-cooperative games and Nash equilibrium which are central to game theory. In addition, as a means of bridging between game theory and their applications in wireless communications, we also spend part of the chapter discussing the issue of computing Nash equilibria via iterative gameplay. The use of myopic decision dynamics, which fall under such iterative processes, has been often adopted when applying game-theoretical approaches to solving wireless communications problems. The approach will be explained here through a series of simple exercises, with the convergence issue demonstrated and discussed.