So far, we have dealt with strategic form games. In strategic form games, all the players are presented as choosing their strategies simultaneously. Therefore, strategic form games hinder an explicit representation of strategic situations in which some of the players act after other players have already chosen their actions, or strategic situations in which some or all of the players act more than once over the course of time.

Games in which the strategic situation is represented as evolving over time are called extensive form games. In the remaining part of the book, we will discuss several types of extensive form games.

First we will deal with games with a finite number of stages, at each of which one of the players chooses between several actions that are available to him. We will then proceed to discuss a more general case – games with a finite number of stages, in which a number of players may simultaneously choose their actions in at least some of the stages of the game. In the sequel, we will address the even more general case of games that may continue over an unbounded number of stages and in which, at any stage of the game, a number of players may choose their actions simultaneously. Finally, we will go on to deal with the particular case of repeated games, in which at every stage of the game all the players repeatedly play one particular strategic form game. We will draw a comparison between the case in which the number of repetitions is finite and the case in which the number of repetitions is unbounded.

All the extensive form games we will discuss in this book are perfect information games: at any stage at which a player or players are called upon to choose their actions, they know what actions all the other players have taken at all precedent stages of the game. The discussion of the more general cases, involving imperfect information, in which certain players possess, at some stages of the game, only partial information on players’ actions in precedent stages, is beyond the scope of this book.