4.2: Strategies in 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.)

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We define a strategy for a player in an extensive-form game as a specification for each of her information sets of the (pure or mixed) action she would take at that information set. One such strategy for each player constitutes a strategy profile for the extensive-form game.

Every extensive-form game can be expressed as a strategic-form game.

We incorporate uncertain exogenous events into the extensive form by introducing Nature as a nonstrategic player who acts randomly. We learn how to construct the strategic-form of an extensive-form game when Nature takes a turn at bat.

We study two different types of randomized strategies in extensive-form games. The behavioral strategy specifies randomizations at each information set independently. The mixed strategy specifies randomizations over pure extensive-form strategies. Behavior strategies do not permit correlations across information sets that mixed strategies allow. However, we show that, in extensive-form games satisfying *perfect recall*, mixed and behavior strategies can be used interchangeably in a precise sense. We learn how to convert back and forth between the two types of randomized strategies.

We define how to restrict an extensive-game strategy to a particular subgame.

Previous section: §4.1: Introduction to Extensive-Form Games |
Course Outline | Next section: §4.3: Solution Concepts in Extensive-Form Games |

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