§ 4.1 Introduction to extensive-form games

A simple extensive-form game
This is a chapter from the graduate-level game-theory course I taught circa 1992–1997. Check out the preface and Table of Contents. I no longer maintain, update, or correct these notes. However, I do appreciate hearing from people who download these notes and find them useful.


When we model a strategic economic situation we want to capture as much of the relevant detail as tractably possible. A game can have a complex temporal and information structure; and this structure could well be very significant to understanding the way the game will be played. These structures are not acknowledged explicitly in the game’s strategic form, so we seek a more inclusive formulation. It would be desirable to include at least the following: 1) the set of players, 2) who moves when and under what circumstances, 3) what actions are available to a player when she is called upon to move, 4) what she knows when she is called upon to move, and 5) what payoff each player receives when the game is played in a particular way. Components 2 and 4 are additions to the strategic-form description; component 3 typically involves more specification in the extensive form than in the strategic form.

We can incorporate all of these features within an extensive-form description of the game. The foundation of the extensive form is a game tree. First I’ll discuss what a tree is and then describe the additional specifications and interpretations we need to make in order to transform it into a full-fledged extensive-form description of the game. We carefully discuss the concept of an information set. We’ll discuss additional restrictions upon the information structure to reflect a common assumption, viz. perfect recall, which asserts that players don’t forget. We’ll discuss the relation between this traditional, graph-theoretic exposition and a more recent one based on the arborescence. After that we’ll learn how to ease our analysis of complicated games by breaking them up into simpler subgames.


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