1. More on Games
April 17, 2013

2. Announcements
• I have homework 1 and 2: come get at end of
class.
• Homework 3 is now posted on website.
• Due at the beginning of class on Monday.

3. Last Class
• Began our discussion about game theory.
• Introduced the concepts of (1) players, (2)
strategies, and (3) payoffs

4. Learning Goals
• Recreate prisoner’s dilemma
• Set penalties to enforce Nash equilibria.
• (Time permitting) Conceptualize how games
change when players move sequentially

5. Prisoner’s Dilemma Redux
• Players: Jake and Lisa
• Strategies: Confess or Deny.
• Payoffs:
– Both confess: 2 years each
– Both deny: 1 year each
– Jake confesses, Lisa denies: Jake 0 years, Lisa 5 years
– Lisa confesses, Jake denies: Jake 5 years, Lisa 0 years

6. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years (J) 1 year (J)
Deny
0 years (L) 1 year(L)

7. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years(J) 1 year (J)
Deny
0 years (L) 1 year(L)
Confess is a dominant strategy for Jake. How about Lisa?

8. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years(J) 1 year (J)
Deny
0 years (L) 1 year(L)
Confess is a dominant strategy for Jake. How about Lisa?

9. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years(J) 1 year (J)
Deny
0 years (L) 1 year(L)
Confess is a dominant strategy for Jake. How about Lisa?

10. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years(J) 1 year (J)
Deny
0 years (L) 1 year(L)
Confess is a dominant strategy for Jake. How about Lisa?

11. The Prisoner’s Dilemma
Remember: Payoffs are sentences; lower is better!
Lisa
Confess Deny
2 years (J) 0 years (J)
Confess
2 years (L) 5 years (L)
Jake
5 years (J) 1 year (J)
Deny
0 years (L) 1 year(L)

12. Payoff Matrix for Advertising Game
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 2 million (Vz)
Spending 1 million (ATT) 0.5 million (ATT)
Verizon
Leave
0.5 million (Vz) 1.5 million (Vz)
Spending
2 million (ATT) 1.5 million (ATT)
Unchanged

13. Payoff Matrix for Advertising Game
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 2 million (Vz)
Spending 1 million (ATT) 0.5 million (ATT)
Verizon
Leave
0.5 million (Vz) 1.5 million (Vz)
Spending
2 million (ATT) 1.5 million (ATT)
Unchanged

14. Payoff Matrix for Advertising Game
Obviously both are better off at (Unchanged,Unchanged). How to get
there?
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 2 million (Vz)
Spending 1 million (ATT) 0.5 million (ATT)
Verizon
Leave
0.5 million (Vz) 1.5 million (Vz)
Spending
2 million (ATT) 1.5 million (ATT)
Unchanged
Contract: I will play ``unchanged.’’ If I cheat, I pay the
other no less than X dollars. What X makes (Unchanged,
Unchanged) a Nash Equilibrium?

15. Last class: What X makes (No Chg, No
Chg) a Nash Equilibrium?
A. 0 million
B. 0.5 million (~30% of class)
C. 1 million (~50% of class)
D. 1.5 million
E. 2 million

16. Payoff Matrix for Advertising Game
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million+X-X(Vz) 2 million-X(Vz)
Spending 1 million+X-X(ATT) 0.5million+X(ATT)
Verizon
Leave
0.5 million+X(Vz) 1.5 million (Vz)
Spending
2 million-X(ATT) 1.5 million (ATT)
Unchanged
Contract: I will play ``unchanged.’’ If I cheat, I pay the
other no less than X dollars. What X makes (Unchanged,
Unchanged) a Nash Equilibrium?

17. Payoff Matrix for Advertising Game:
X=1 million.
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 1 million (Vz)
Spending 1 million (ATT) 1.5million (ATT)
Verizon
Leave
1.5 million (Vz) 1.5 million (Vz)
Spending
1 million (ATT) 1.5 million (ATT)
Unchanged

18. Payoff Matrix for Advertising Game:
X=1 million.
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 1 million (Vz)
Spending 1 million (ATT) 1.5million (ATT)
Verizon
Leave
1.5 million (Vz) 1.5 million (Vz)
Spending
1 million (ATT) 1.5 million (ATT)
Unchanged

19. OK, this is technically correct.
• But why use a sledgehammer when you can
use a chisel?
• Note, with a 1 million penalty, (Unch,Unch) is
Nash, but also dominant.
• What is the smallest penaltynecessary?

20. Payoff Matrix for Advertising Game
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million+X-X(Vz) 2 million-X(Vz)
Spending 1 million+X-X(ATT) 0.5million+X(ATT)
Verizon
Leave
0.5 million+X(Vz) 1.5 million (Vz)
Spending
2 million-X(ATT) 1.5 million (ATT)
Unchanged
Contract: I will play ``unchanged.’’ If I cheat, I pay the
other no less than X dollars. What X makes (Unchanged,
Unchanged) a Nash Equilibrium?

21. Payoff Matrix for Advertising Game:
X=0.5 million.
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 1.5 million (Vz)
Spending 1 million (ATT) 1million (ATT)
Verizon
Leave
1 million (Vz) 1.5 million (Vz)
Spending
1.5 million (ATT) 1.5 million (ATT)
Unchanged

22. Payoff Matrix for Advertising Game:
X=0.5 million.
AT&T
Leave Spending
Increase Spending
Unchanged
Increase 1 million (Vz) 1.5 million (Vz)
Spending 1 million (ATT) 1million (ATT)
Verizon
Leave
1 million (Vz) 1.5 million (Vz)
Spending
1.5 million (ATT) 1.5 million (ATT)
Unchanged
Whoa! cool!

23. The Economics of Cartels
• Cartel: any group of firms that agree to restrict output for the
purpose of earning an economic profit.
• But cartels are notoriously hard to maintain. Why?
• Example: oligopolists Boeing and Airbus
P
$1 million
Profit MC=ATC
$600 million
MR D
1000 Q (in thousands)

24. Payoff Matrix for a Cartel Agreement
Boeing
P=$1 million P=$999,999
(Cooperate) (Defect)
P=$1 million $300 million (A) 0 (A)
(Cooperate) $300 million (B) ≈$600 million (B)
Airbus
P=$999,999 ≈$600 million (A) ˂$300million (A)
(Defect) 0 (B) ˂$300 million (B)
Contract for at least how much of a penalty for defecting?

25. Let’s Play a Game
• I need 10 volunteers.
• Each person: Write your name and a number
between 0 and 100. The cards will be
collected and the numbers averaged. The
number closest to exactly half of the average
is the winner.
• I predict the winner is near ___. Am I right?

26. Second Round
• I need 10 volunteers.
• Each person: Write your name and a number
between 0 and 100. The cards will be
collected and the numbers averaged. The
number closest to exactly half of the average
is the winner.
• I predict the winner is near ___. Am I right?

27. Third Round
• I need 10 volunteers.
• Each person: Write your name and a number
between 0 and 100. The cards will be
collected and the numbers averaged. The
number closest to exactly half of the average
is the winner.
• I predict the winner is near ___. Am I right?

28. What is the Nash Equilibrium?
Can someone give an answer and explain?

29. Games in Which Timing Matters
Opening a New Restaurant
Alice and Bill are each considering opening a restaurant in
their local neighborhood . . . But what kind?
Bill
Dinner Breakfast
$1000 (A) $1600 (A)
Dinner
$1000 (B) $1400 (B)
Alice
$1400 (A) $800 (A)
Breakfast
$1600 (B) $800 (B)

30. Decision Tree
$1000 (A)
D $1000 (B)
D B $1400 (A)
$1600 (B)
$1600 (A)
D $1400 (B)
B
B $800 (A)
$800 (B)
Bill Alice Outcome
Decides Decides