Introduction to Game Theory

Game theory mathematically models strategic interaction among intelligent decision-makers. It has wide applications in economics, sociology, psychology, political science, biology, and as we will introduce later in this book, cybersecurity. To facilitate the readers, we present the basics of game theory in this chapter. We will start by introducing two-player zero-sum normal-form games, the basic class of games that involve two decision-makers who will each make a single move at the same time, and get a payoff, with the two players' payoffs summing up to zero. We will then introduce the solution concepts in normal-form games, including the most well-known Nash equilibrium concept. We further introduce the extensive-form games, which are more complicated and more expressive than normal-form games. They explicitly represent the sequencing of players' moves and the information each player has about the other players' moves when they make a decision. We will then introduce Stackelberg games and Stackelberg security games, a subclass of games with wide applications in security domains. We will also introduce repeated games where the players repeatedly play the same game. Finally, we will add Bayesian games that depict the uncertainty in players' types and payoff and stochastic games that capture the dynamic transition from one game to another. These models and concepts will be used frequently in later chapters.