1. Today: Some classic games in game theory
More game theory
Today: Some classic games in game theory

2. Last time… Introduction to game theory
Games have players, strategies, and payoffs
Based on a payoff matrix with simultaneous decisions, we can find Nash equilibria (NE)
In sequential games, some NE can be ruled out if people are rational

3. Today, some classic game theory games
Games with inefficient equilibria
Prisoner’s Dilemma
Public Goods game
Coordination games
Battle of the Sexes
Chicken
Zero-sum game
Matching pennies
Animal behavior
Subordinate pig/Dominant pig

4. Prisoner’s dilemma Yes No –1, –1 +3, –6 –6, +3 +1, +1
Player 2
Why is this game called prisoner’s dilemma?
Think about a pair of criminals that have a choice of whether or not to confess to a crime
Yes No
–1, –1
+3, –6
–6, +3
+1, +1
Player 1

5. Prisoner’s dilemma What is the NE? Yes No –1, –1 +3, –6 –6, +3 +1, +1
Player 2
What is the NE?
Let’s underline
Yes No
–1, –1
+3, –6
–6, +3
+1, +1
Player 1

6. Prisoner’s dilemma Yes No –1, –1 +3, –6 –6, +3 +1, +1 What is the NE?
Player 2
What is the NE?
Let’s underline
Each player has a dominant strategy of choosing Yes
However, both players get a better payout if each chooses No
Yes No
–1, –1
+3, –6
–6, +3
+1, +1
Player 1

7. Prisoner’s dilemma and cartels
Cartels are usually unstable since each firm has a dominant strategy to charge a lower price and sell more
See Table 11.4 (p. 327) for an example

8. Public goods game
You can decide whether or not you want to contribute to a new flower garden at a local park
If you decide Yes, you will lose $200, but every other person in the city you live in will gain $10 in benefits from the park
If you decide No, you will cause no change to the outcome of you or other people

9. Public goods game
What is each person’s best response, given the decision of others?
We need to look at each person’s marginal gain and loss (if any)
Choose yes  Gain $10, lose $200
Choose no  Gain $0, lose $0

10. Public goods game Which is the better choice?
Choose no (Gain nothing vs. net loss of $190)
NE has everybody choosing no
Efficient outcome has everybody choosing yes
Why the difference?
Each person does not account for others’ benefits when making their own decision

11. Battle of the Sexes Bar Play +3, +1 +0, +0 +1, +3
Player 2
Neither person knows where the other is going until each person shows up
If both people show up at the same place, they enjoy each other’s company (+1 for each)
Bar
Play
+3, +1
+0, +0
+1, +3
Player 1
Two people plan a date, and each knows that the date is either at the bar or a play

12. Battle of the Sexes: Other things to note
Player 2
Player 1 gets additional enjoyment from the bar if Player 2 is there too, since Player 1 likes the bar more
Player 2 enjoys the play more than Player 1 if both show up there
As before, we underline the best strategy, given the strategy of the other player
Bar
Play
+3, +1
+0, +0
+1, +3
Player 1

13. Battle of the Sexes Two NE
Player 2
Two NE
(Bar, Bar)
(Play, Play)
As in cases before when there are multiple NE, we cannot determine which outcome will actually occur
Bar
Play
+3, +1
+0, +0
+1, +3
Player 1

14. Battle of the Sexes
Player 2
Battle of the Sexes is known as a coordination game
Both get a positive payout if they show up to the same place
Bar
Play
+3, +1
+0, +0
+1, +3
Player 1

15. Chicken Two cars drive toward each other
If neither car swerves, both drivers sustain damage to themselves and their cars
If only one person swerves, this person is known forever more as “Chicken”

16. Chicken Swerve Straight +0, +0 –1, +1 +1, –1 –10, –10
Player 2
Swerve
Straight
+0, +0
–1, +1
+1, –1
–10, –10
Player 1
Next step: Underline as before

17. Chicken Swerve Straight +0, +0 –1, +1 +1, –1 –10, –10
Player 2
Swerve
Straight
+0, +0
–1, +1
+1, –1
–10, –10
Player 1
Notice there are 2 NE
One player swerves and the other goes straight
This game is sometimes referred to as an “anti-coordination” game
NE results from each player making a different decision

18. Matching pennies If both choices match, Player 1 wins
If both choices differ, Player 2 wins
This is an example of a zero-sum game, since the sum of each box is zero
Heads
Tails
+1, –1
–1, +1
Player 1
Two players each choose Heads or Tails

19. Matching pennies A characteristic of zero-sum games Heads Tails +1, –1
Player 2
A characteristic of zero-sum games
Whenever I win, the other player must lose
Heads
Tails
+1, –1
–1, +1
Player 1
Underlining shows no NE

20. Subordinate pig/Dominant pig
Two pigs are placed in a cage
Left end of cage: Lever to release food
12 units of food released when lever is pressed
Right end of cage: Food is dispensed here

21. Subordinate pig/Dominant pig
If both press lever at the same time, the subordinate pig can run faster and eat 4 units of food before the dominant pig “hogs” the rest
If only the dominant pig presses the lever, the subordinate pig eats 10 of the 12 units of food
If only the subordinate pig presses the lever, the dominant pig eats all 12 units
Pressing the lever exerts a unit of food

22. Subordinate pig/Dominant pig
Who do you think will get more food in equilibrium?
Who thinks ?
Who thinks ?

23. Subordinate pig/Dominant pig
The numbers on the previous slide translate to the payoff matrix seen
dominant pig
Yes No
3, 7
–1, 12
10, 1
0, 0
subordinate pig
Next: Underline test

24. Subordinate pig/Dominant pig
In Nash equilibrium, the dominant pig always gets the lower payout
Why?
The subordinate pig has a dominant strategy: No
The dominant pig, knowing that the subordinate pig will not press the lever, will want to press the lever
dominant pig
Yes No
3, 7
–1, 12
10, 1
0, 0
subordinate pig
Exactly 1 NE
The dominant pig presses lever

25. Do people always play as Nash equilibrium predicts?No
Many papers have shown that people often are not selfish, and donate into public goods
Norms are often established to make sure that people are encouraged to act in the best interest of society

26. Summary Today, we looked at some well-known games
Some games have NE; others do not
However, people do not always behave as NE would predict