Extensive Form Games

1. Extensive Form Games Econ 171

2. Reminder: Course requirements • Class website Go to economics department home page. Under Links, find Class pages, then click on Econ 171 • Textbook: Games, Strategies, and Decision Making  by Joseph E. Harrington, Jr. • Clicker: Available at campus bookstore i>clicker Register your clicker at www.i>clicker.com/registration

3. Checkup on Assigned Reading Describe the Matching Pennies game that we discussed on Tuesday in extensive form notation.

4. Clicker Test(to check that you are registered) Do you have a working i>clicker with you? • Yes • No, I just clicked my ballpoint pen.

5. Details of strategic form game • Set of Players • For each player a strategy set—list of all the strategies that the player could choose. Remember that a strategy tells everything you would on any occasion when its your turn. • Strategy profile: List of strategies chosen by every player. • Payoff to each player depends on the strategy profile that was chosen.

6. Two player game matrix in strategic form Make a two-by-two table with one row for each strategy that player 1 could choose and one column for every strategy that player 2 could choose. Enter payoffs to players 1 and 2 in appropriate spots.

7. Example: Matching Pennies • In this case each player has only two possible strategies. Choose Heads, Choose tails. • Payoff to Player 1 (row chooser) is written first, then payoff to Player 2.

8. Matching PenniesStrategic Form of Game Player 2 Tails Heads Heads Player 1 Tails

9. More complicated game Player 1 C D Player 2 2 0 E F Player 1 3 1 G H 0 0 1 2 4 Possible Strategies for Player 1 : What are they? 2 Possible Strategies for Player 2: What are they?

10. Strategic Form Player 2 E F C,G C,H Player 1 D,G D,H

11. WMDs: What are the strategies?

12. Prisoners’ Dilemma Game Player 2 Cooperate Defect P LAyER 1 Cooperate Defect

13. The game of Chicken James Dean story. Alternatively—Two animals both want a resource. Each has two possible strategies. Fight or give up. A fight is very bad for both of them. How do we make an interesting game of this?

14. Battle of the sexes Alice and Bob love to be together, but they don’t agree about where. Stereotypic version. Alice loves opera. Bob loves fights. Each would rather be together at less preferred event than to be apart, but each would prefer favorite event.

15. Cournot Equilibrium Two firms each choose quantity. Price is lower the greater is total output. Profits of a firm are price times its own quantity minus costs.