Jim Ratliff's Game Theory Course:
4.1 Introduction to Extensive-Form Games

This is a chapter from Jim Ratliff's Graduate-Level Game-Theory Course. See outline for the entire course. I no longer maintain, update, or correct these notes. However, I would appreciate hearing from people who download these notes and find them useful. Also I may eventually post problem sets and their solutions. Let me know if you'd like to be notified of such changes. (Please email me.)

Abstract

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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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§3.2: Computing Mixed-Strategy Nash Equilibria of 2x2 Strategic-Form Games
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§4.2: Strategies in Extensive-Form Games


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