1. - The Lockhorns Cartoon
Game Theory
“Loretta’s Driving Because I’m Drinking and I’m Drinking Because She’s Driving”
- The Lockhorns Cartoon
Mike Shor
Lecture 3

2. Review Understand the game you are in Note if the rules are flexible
Anticipate your opponents’ reactions
Understand the assumptions
Recognize that not everyone else understands them
Game Theory - Mike Shor

3. Game Theory - Mike Shor

4. Equilibrium Nash Equilibrium: Best Response:
A set of strategies, one for each player, such that each player’s strategy is best for her given that all other players are playing their equilibrium strategies
Best Response:
The best strategy I can play given the strategy choices of all other players
Everybody is playing a best response
No incentive to unilaterally change my strategy
Game Theory - Mike Shor

5. Identifying the Equilibrium
Pure strategy equilibrium
Consider mixed later
Dominance
Dominance solvable
Only one dominant strategy
Successive elimination of dominated strategies
Cell-by-cell inspection
Game Theory - Mike Shor

6. Cigarette Advertising on TV
All US tobacco companies advertised heavily on TV
Surgeon General issues official warning
Cigarette smoking may be hazardous
Cigarette companies’ reaction
Fear of potential liability lawsuits
Companies strike agreement
Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.
1964
1970
Game Theory - Mike Shor

7. Strategic Interactions
Players: Reynolds and Philip Morris
Strategies: { Advertise , Do Not Advertise }
Payoffs: Companies’ Profits
Each firm earns $50 million from its customers
Advertising costs a firm $20 million
Advertising captures $30 million from competitor
How to represent this game?
Game Theory - Mike Shor

8. Normal (Strategic) Form
PLAYERS
Philip Morris
No Ad Ad
Reynolds
50 , 50
20 , 60
60 , 20
30 , 30
STRATEGIES
PAYOFFS
Game Theory - Mike Shor

9. Normal Form Best reply for Reynolds: Advertise!
If Philip Morris advertises: advertise
If Philip Morris does not advertise: advertise
Regardless of what you think Philip Morris will do
Advertise!
Philip Morris
No Ad Ad
Reynolds
50 , 50
20 , 60
60 , 20
30 , 30
Game Theory - Mike Shor

10. Dominant Strategy
A strategy that outperforms all other choices no matter what opposing players do
Firm 1’s strategies: { A, B, C }
Firm 2’s strategies: { X, Y, Z }
C is strictly dominant for Firm 1 if:
P(C,X)>P(A,X) P(C,X)>P(B,X)
P(C,Y)>P(A,Y) P(C,Y)>P(B,Y)
P(C,Z)>P(A,Z) P(C,Z)>P(B,Z)
C is weakly dominant for Firm 1 if:
Some inequalities are weak (), at least one is strong(>)
Game Theory - Mike Shor

11. Dominance Solvable
If each player has a dominant strategy, the game is dominance solvable
What is the equilibrium of the cigarette advertising game?
COMMANDMENT
If you have a dominant strategy, use it.
Expect your opponent to use her dominant strategy if she has one.
Game Theory - Mike Shor

12. Cigarette Advertising
After the 1970 agreement, cigarette advertising decreased by $63 million
Profits rose by $91 million
Prisoner’s Dilemma
An equilibrium is NOT necessarily efficient
What if the game is not dominance solvable?
Game Theory - Mike Shor

13. Two firms competing over sales
A Strategic Situation
Two firms competing over sales
Time and The Economist must decide upon the cover story to run some week.
The big stories of the week are:
A presidential scandal (labeled S), and
A proposal to deploy US forces to Grenada (G)
Neither knows which story the other magazine will choose to run
Game Theory - Mike Shor

14. One Dominant Strategy Who has a dominant strategy?
The Economist G S
Time
100 , 100
0 , 90
95 , 100
95 , 90
Who has a dominant strategy?
Assume it will be played!
Other player can plan accordingly.
Game Theory - Mike Shor

15. Dominated Strategies The Economist G S Time 100 , 100 0 , 90 95 , 100
0 , 90
95 , 100
95 , 90
For The Economist: G dominant = S dominated
Dominated Strategy:
There exists another strategy which always does better regardless of opponents’ actions
Game Theory - Mike Shor

16. Successive Elimination of Dominated Strategies
If a strategy is dominated, eliminate it
The size and complexity of the game is reduced
Eliminate any dominant strategies from the reduced game
Continue doing so successively
Game Theory - Mike Shor

17. Example: Tourists & Natives
Two bars (bar 1, bar 2) compete
Can charge price of $2, $4, or $5
6000 tourists pick a bar randomly
4000 natives select the lowest price bar
Bar 2 $2 $4 $5
Bar 1
10 , 10
14 , 12
14 , 15
12 , 14
20 , 20
28 , 15
15 , 14
15 , 28
25 , 25
Game Theory - Mike Shor

18. Successive Elimination of Dominated Strategies
Does any player have a dominant strategy?
Does any player have a dominated strategy?
Eliminate the dominated strategies
Reduce the normal-form game
Iterate the above procedure
What is the equilibrium?
Game Theory - Mike Shor

19. Successive Elimination of Dominated Strategies
Bar 2 $2 $4 $5 $2 10 , , 10 14 , , 12 14 , , 15
Bar 1
Bar 1 $4 12 , , 14 20 , , 20 28 , , 15 $5 15 , , 14 15 , , 28 25 , , 25
Bar 2 $4 $5
Bar 1
20 , 20
28 , 15
15 , 28
25 , 25
Game Theory - Mike Shor

20. No Dominated Strategies
Often there are no dominated strategies
Or: reducing the game is not sufficient
There may be multiple equilibria
Method:
Cell-by-cell inspection
Ask:
Is each player playing the best response to the other player?
Game Theory - Mike Shor

21. Types of Games Games of Assurance Games of Coordination
Games of Chicken
Game Theory - Mike Shor

22. Games of Assurance Two firms each earning $45,000
Both can invest the $45,000 into R&D
R&D successful only if both invest
If R&D successful, each earns $95,000
Firm 2
Invest
Don’t
Firm 1
50 , 50
0 , 45
45 , 0
45 , 45
Game Theory - Mike Shor

23. Cell-by-cell Inspection
Consider { Invest , Don’t }
Both players have an incentive to change their strategy: NOT an equilibrium
Firm 2
Invest
Don’t
Firm 1
50 , 50
0 , 45
45 , 0
45 , 45
Game Theory - Mike Shor

24. Assurance Outcomes Two equilibria exist
Both firms prefer (I ,I) to (D,D)
Payoffs of 50 to each firm instead of 45
However, investing is risky
Must have assurances
How to achieve assurance?
Strategic moves: commit to choosing I
Sequential moves: leader chooses the equilibrium
Game Theory - Mike Shor

25. Games of Coordination Joint ventures and the choice of supplier
Two firms engaged in joint venture
Must use the same supplier, but each firm has a preferred supplier
Firm 2 A B
Firm 1
100 , 50
0 , 0
50 , 100
Game Theory - Mike Shor

26. Coordination Outcomes
Two equilibria exist
Firms prefer different equilibria
How to achieve the most desirable outcome for you?
Strategic moves: commit to choosing A
Sequential moves: leader chooses the equilibrium
Game Theory - Mike Shor

27. Summary You must put yourself in your rival’s shoes
Recognize dominant and dominated strategies
Anticipate that your opponent will recognize them as well
Game Theory - Mike Shor