{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

LectureFeb15_MATH4321_12S

# LectureFeb15_MATH4321_12S - Reduction of a Game in...

This preview shows pages 1–9. Sign up to view the full content.

Reduction of a Game in Extensive Form to Strategic Form. Pure strategy . A pure strategy is a player’s complete plan for playing the game. It should cover every contingency. A pure strategy for a Player is a rule that tells him exactly what move to make in each of his information sets. It should specify a particular edge leading out from each information set.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Player I has 3 information sets. The set of edges coming out from the information sets are{A,B}, {E,F}, {C,D}. Player II has two information sets. The set of edges coming out from the information sets are {a,b}, {c,d}. Set of Pure Strategies for I: {A,B}x{C,D}x{E.F} ={ACE, ACF, ADE, ADF, BCE, BCF, BDE, BDF} Set of Pure Strategies for II: {a,b}x{c,d}={ac,ad,bc,bd}
Remark : Even for a simple game, there may be a large number of pure strategies. Example : (Two move Tic-Tac-Toe) Player I and II take turn to make a move on the Tic-Tac-Toe board. The game stops after each player has made one move. How many pure strategies are there for Player I and for Player II?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example : (Two move chess) There are 20 possible moves for Player I and 20 possible moves for Player II. How many pure strategies are there for Player II?
Reduced pure strategy : Specification of choices at all information sets except those that are eliminated by the previous moves. Remark : It is not too easy to find the set of reduced pure strategies. Also we need to use full pure strategies for another important concept.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Set of Reduced Pure Strategies for I:{AE, AF, BC, BD} Set of Reduced Pure Strategies for II: {ac,ad,bc,bd}
Now that we have set of pure strategies for each player, we need to find the payoffs to put the game in strategic form. Random payoffs . The actual outcome of the game for given pure strategies of the players depends on the chance moves selected, and is therefore a random quantity. We represent random payoffs by their average values.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Suppose Player I uses BCF and Player II uses ac.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}