1. Managerial Economics Kyle Anderson
Game Theory
Managerial Economics
Kyle Anderson
Indiana University
Kelley School of Business

2. Grading scheme: Choose a plan, Red or Blue.
Matched with a classmate (anonymously).
If you both choose the blue grade scheme, you both get an A-.
If you both choose the red grade scheme, you both get a B.
If you choose the blue scheme and your matched partner chooses red, you get a B- and your partner gets an A.
If you choose the red scheme and your matched partner chooses blue, you get an A and your partner gets a B-.
Which grade scheme do you choose?

3. Grading Game B+, B+ B-, A A, B- B, B Player 2 Two players
Simultaneous moves
Perfect information
One-time game
Blue
Red
B+, B+
B-, A
A, B-
B, B
Player 1
Normal form

4. Grading Game 3, 3 1, 4 4, 1 2, 2 Player 2 Blue Red Player 1
Red is the better strategy for Player 1, regardless of what Player 2 does. Dominant Strategy Player 2 has the same dominant strategy. Nash Equilibrium – each player is doing as well as it can do given its rivals actions.
Player 2
Blue
Red
3, 3
1, 4
4, 1
2, 2
Player 1
Normal form
A = 4, B+ = 3, B = 2, B- = 1

5. Nature of a game Frequency of movement Elements Nature of movement
One-shot game
Finitely repeated game
Infinitely repeated game
Nature of movement
Simultaneous-move game
Sequential move game
Elements
Players
Strategies
Payoffs
Information
Rationality

6. Pricing Game Simultaneous move, one-shot game
Two firms, each firm picks a price level (high or low), products are close substitutes.
Firms have some fixed costs.

7. Pricing Game 0, 0 40, -10 -10, 40 10, 10 Heron low price
Heron high price
Anderson low price
0, 0
40, -10
Anderson high price
-10, 40
10, 10
What strategies should the firms’ pursue?
*Anderson’s payoff is listed first, followed by Heron

8. Prisoners’ Dilemma
Heron low price
Heron high price
Anderson low price
0, 0
40, -10
Anderson high price
-10, 40
10, 10
One or more of the firms has a dominant strategy.
Pursuing the dominant strategy leads to an outcome that is sub-optimal for the players.
Of course, what is sub-optimal for the firm(s) may be optimal for others (i.e. customers).

9. Games with 3 or more options
Bar 2 $2 $4 $5
Bar 1
10 , 10
14 , 12
14 , 15
12 , 14
20 , 20
28 , 13
15 , 14
13 , 28
25 , 25
in thousands of dollars
If P2 plays $2: 5 > 4 > 2
Dominated Strategy: one that always leads to a lower payout than another available strategy.
If P2 plays $4: 4 > 2 > 5
If P2 plays $5: 4 > 5 > 2

10. Simultaneous Move Game
Two players, each with a choice between Yellow and Blue.
If they both make the same choice, they earn $1.
If they don’t match, they earn $0.
September 21, 2018

11. Coordination Game
Yellow
Blue
1, 1
0, 0
How many NEs are there?

12. Simultaneous Move Game
Two players, each with a choice between Yellow and Blue.
If they both choose Yellow, Player 1 gets $5 and Player 2 gets $1.
If they both choose Blue, Player 1 gets $1 and Player 2 gets $5.
If they don’t match, they earn $0.
September 21, 2018

13. Coordination Game, sort of
Player 2
Yellow
Blue
Player 1
5, 1
0, 0
1, 5
How many NEs are there?

14. Monitoring Game -1, 0 2, -5 0, 0 -2, 2 Business Pay taxes
Shirk on taxes
IRS
audit
-1, 0
2, -5
don’t audit
0, 0
-2, 2
How many NEs are there?
There are no pure strategy NEs
There is a mixed (randomized) strategy NE

15. Repeated Pricing Game 0, 0 40, -10 -10, 40 10, 10 Heron low price
Heron high price
Anderson low price
0, 0
40, -10
Anderson high price
-10, 40
10, 10
What strategies should the firm’s pursue?
*Anderson’s payoff is listed first, followed by Heron

16. Infinitely repeated game
Cooperation may occur if the benefits of cooperating exceed benefits of cheating.
Compare PV of cooperating with PV of cheating.
Does it pay?
Prof(cheat) = πcheat + πNash + πNash…
Prof(coop) = πcoop + πcoop + πcoop…

17. Infinitely repeated game
Does cooperation pay?
As long as the discount rate is less than 1/3 (33%), then it is better to cooperate.

18. Simultaneous move games
Why do hotels franchise?
Compare NE in one-shot vs. repeated.
Hotel – decent quality
Hotel – low quality
Stay
5, 5
-10, 10
Don’t stay
0, -5
0, 0

19. Sequential move games Accommodate 10, 10 Price War -10, 5 Enter
Incumbnt
Price War
-10, 5
Enter
Accommodate
0, 20
Don’t
Newbie
Incumbnt
0, 8
Price War
Solve by Backward Induction – Last stage first
What outcome do we expect?
*Payoffs for Newbie are listed first

20. Three stage game What outcome do we expect? Can Player 1 do better?
Fight
-5, -10
Defend 1 2
Attack
-1, 9
Retreat 1
Surrender
10, -5
Don’t
0, 10
What outcome do we expect? Can Player 1 do better?

21. Integer game
Strategically choose an integer between Submit that number to me. I will calculate the average of all the numbers. The winning number will be the number that is 2/3 of the average of all submissions. I will pay the winner $10.

22. Division game
There is a potential joint venture between player 1 and player 2. The joint venture will net a total of $10. Player 1 gets to choose how that $10 is divided between the two players. Player 2 can then either accept or reject the offer. The game then ends without any negotiation.
Kyle Anderson
September 21, 2018