1: What is Game Theory?

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“Game Theory is not about 'playing games.' It is about conflict resolution among rational but distrustful beings.” Poundstone, Prisoner's Dilemma, p. \(39\).

Although we will play many games throughout this book, our goal is to understand how rational, distrustful players would play the game. These games are meant to serve as models for situations of conflict. We will explore how to “solve” games under certain assumptions about our players. As with any mathematical model, we will need to make assumptions about how our players will behave, what information they have, and the constraints of the game. For example, we will assume that our players will use all information available to them, and that players will follow the rules of the game.

Games can provide hours of recreational enjoyment, and are worth studying for this alone. However, even simple games can be used to model political, social, and economic interactions. Understanding some foundations of game theory can help us interpret, predict, and respond in competitive situations.

1.1: Players and Strategies
In this book, most of the games will be played by two players. Each player must decide how he or she will play the game. In order to study games mathematically, we need to make some assumptions about how the players should play the game. This allows us to be able to better predict what our players should do. The example given in this section illustrates the characteristics we will assume about our players.
1.2: Game Matrices and Payoff Vectors
We need a way to describe the possible choices for the players and the outcomes of those choices. For now, we will stick with games that have only two players. We will call them Player 1 and Player 2.