In cognitive radio networks, there are many secondary users, as well as possible attackers; each has its own action and payoff and can be considered as a rational agent, as long as secondary users are usually equipped with powerful computing devices. Hence, it is natural to introduce game theory, which traces back to early 1900s  and analyzes the possible conflict or collaboration and the corresponding strategies of rational players, to study the interactions among the agents in the cognitive radio network. In this section, we introduce the basic concepts in game theory. There are many types of games, such as the strategic-form games, repeated games, stochastic games, and differential games, etc. A comprehensive introduction of game theory can be found in . A more modern introduction to game theory, from the computer science perspective, can be found in . Games in dynamical systems, such as Markov processes or continuous time systems, are discussed in  and . As a preliminary introduction to game theory, we focus on the simplest strategic-form game in this book, which provides a starting point for studying more complicated games, and then provide a brief introduction to Bayesian games and stochastic games which are carried out in multiple stages.
For simplicity, we assume that there are two players in the game. It is not difficult to extend the two-player game to the general ...