1. Games with Simultaneous Moves I :Discrete Strategies

2. Outline Games with simultaneous moves Nash Equilibrium Dominance
Minimax in Zero-sum Game
Three Players
Multiple/Zero Equilibria in pure strategies
Tree Forms into Strategic Forms

3. Games with Simultaneous Moves
Strategy vs. action
Discrete/Continuous strategy

4. Games in normal (strategic) form.
Games Table/ Game Matrix/ Payoff Table
Column
Left
Middle
Right
Row
Top
3, 1
2, 3
10, 2
High
4, 5
3, 0
6, 4
Low
2, 2
5, 4
12, 3
Bottom
5, 6
9, 7

5. Zero-sum Game
Column
Run
Pass
Blitz
OFFENSE 2 5 13
Short Pass 6
5.6
10.5
Medium Pass
4.5 1
Long Pass 10 3 -2

6. Nash Equilibrium What is Equilibrium?
Cell-by-cell-inspection or enumeration
Best Response Analysis
Column
Left
Middle
Right
Row
Top
3, 1
2, 3
10, 2
High
4, 5
3, 0
6, 4
Low
2, 2
5, 4
12, 3
Bottom
5, 6
9, 7

7. Column
Left
Middle
Right
Row
Top
3, 1
2, 3
10, 2
High
4, 5
3, 0
6, 4
Low
2, 2
5, 4
12, 3
Bottom
5, 6
9, 7

8. The N.E is (Low, Middle) →(5, 4)
A Nash Equilibrium in a game is a list of strategies, one for each player, such that no player can get a better payoff by switching to some other strategy that is available to her while all the other players adhere to the strategies specified for them in the list.

9. A N.E. does not have to be jointly best for the players.
EX: Prisoner’s dilemma
WIFE
Confess
(Defect)
Deny
(Cooperate)
HUSBAND
10yr, 10yr
1yr, 25yr
25yr, 1yr
3yr, 3yr

10. Nash Equilibrium as a system of beliefs
Nash Equilibrium is a set of strategies, such that
(1)each player has correct beliefs about the strategies of the others
(2)the strategy of each is the best for herself, given her beliefs about the strategies of the others

11. Dominance WIFE Confess (Defect) Deny (Cooperate) HUSBAND 10yr, 10yr
Dominant strategy is an action clearly best for a player, no matter what the others might be doing.
“Confess” is a dominant strategy for the husband, while “Confess” is also a dominant strategy for the wife. NE: (Confess, Confess) →(10yr, 10yr)

12. (A,B,…..) are strategies for Player 1.
A is a dominant strategy for Player 1.
A dominates B/C/D….
B/C/D… is a dominated strategy for Player 1.

13. Both (all) Players Have Dominant Strategies
One Player has a Dominant Strategy
FED
Low interest rate
High interest rate
CONGRESS
Budget balance
3, 4
1, 3
Budget deficit
4, 1
2, 2

14. Successive (Iterated) Elimination of Dominated Strategies
Left
Middle
Right Up
5, 2
2, 3
3, 4
Medium
4, 1
3, 2
4, 0
Down
3, 3
1, 2
2, 2

15. MiniMax Method for Zero-Sum Games
MiniMax/Maximin
Column
Run
Pass
Blitz
OFFENSE 2 5 13
Short Pass 6
5.6
10.5
Medium Pass
4.5 1
Long Pass 10 3 -2

16. Three Players TALIA chooses C TALIA chooses NC NINA C NC EMILY 5, 5, 5
3, 6, 3
6, 3, 3
4, 4, 1
NINA C NC
EMILY
3, 3, 6
1, 4, 4
4, 1, 4
2, 2, 2

17. Three Players TALIA chooses D TALIA chooses ND NINA D ND EMILY 2, 7, 2
3, 2, 2
5, 1, 2
2, 5, 2
NINA D ND
EMILY
3, 3, 3
1, 2, 3
2, 1, 1
2, 2, 1

18. Multiple Equilibria in Pure Strategies
Coordination Games
Battle of the Sexes
SALLY
Starbucks
Banyan
HARRY
2, 1
0, 0
1, 2

19. Convergence of expectation Assurance Games
Focal Point
Convergence of expectation
Assurance Games
DEAN
Swerve
(Chicken)
Straight
(Tough)
JAMES
0, 0
-1, 1
1, -1
-2, -2

20. No Equilibrium in Pure Strategies
Rock-Paper-Scissors
Rock
Paper
Scissors
0, 0
-1, 1
1, -1
N.E exists in mixed Strategies

21. Homework, Ch4
question 3, 6, 11, and 12(a & b)

22. Tree form into a strategic formL
(3, 1) U 2 R
(2, 2) 1 D L
(1, 3) R
(4, 1) 2 LL LR RL RR U
3, 1
2, 2 D
1, 3
4, 1 LL LR RL RR U D

23. Minimax/Maximin vs. Nash Equilibrium Revisited