Game theory was conceived as a tool to explain, predict, and guide behavior in strategic interactions among individuals, and its main applications still lie in this domain. But game theory is less wedded to a particular set of questions than is social choice theory, and it has applications to such disparate phenomena as computer programming and biological evolution. Game theory might indeed be regarded as a branch of mathematics rather than as specifically a theory of interactive decision making. However, in this chapter we will focus exclusively on applications of game theory to strategic interactions among individuals. An interaction among individuals is “strategic” if the payoffs to some individuals depend on the choices of others.

What Is a Game?

A game is defined by its players, the strategies that are available to the players, the payoffs to the players from each combination of strategies, and the capacities of the players, including especially the knowledge each player has concerning the other features of the game. Each of the italicized terms has a technical meaning. In the case of the games we shall consider, players are simply people. To keep things simple, we shall for the most part discuss games with only two players. A specific strategy for a player is a complete specification of what actions the player will take whenever the player gets to act. The specification of the strategies available to a player defines all possible actions that the player can take.