1. Game Theory: Refinements
April 19, 2013

2. Announcements
• Homework 3 is due before class on Monday
• Next week we’ll begin talking about
externalities

3. Last Class
• Considered more example of Nash equilibria
and strictly dominant strategies
• Played a game: Write down ½ of the average
of others’ guesses. Choose from [0,100].
– Nash equilibrium: Everyone writes down zero

4. How did we solve this problem?
• If everyone guessed 100, the best number to
write down (best response!) would be 50.
• But if everyone wrote 50, the BR is 25.
• If all 25, BR is 12.5, … etc
• If all 0, BR is 0. Only Nash Equilibrium
• This iterative process for finding equilibrium is
a ``refinement’’ of Nash equilibrium.

5. Refinements
• Extensions of the basic version of Nash
Equilibrium we have seen.
• The game we played demonstrates a concept
called iterated dominance.
• Another refinement has to do with the timing
of the game; called sequential rationality.

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

7. Decision Tree & Backward Induction
Bill
Decides
Alice
Decides
Outcome
D
D
D
B
B
B
$1000 (A)
$1000 (B)
$1600 (A)
$1400 (B)
$1400 (A)
$1600 (B)
$800 (A)
$800 (B)

8. A. To Bed, Tantrum
B. To Bed, Not Tantrum
C. Not to Bed, Tantrum
D. Not to Bed, Not Tantrum

9. Games in Which Timing Matters
Opening a Convenience Store
Freeway
1 mile
1,200 people
A B
C
⅓ mile
400 people
⅓ mile
400 people
⅓ mile
400 people
1 mile
1,200 people
Store A opens first . . . Where should the
owner of a second convenience store choose
to locate?
Monopolistic
competition

10. Tendency for Monopolistic
Competitors to Cluster
Hotelling’s (1929) insights help explain
• Why convenience stores and gas stations are often clustered
on the same corner.
• Why political candidates often “moderates”.
• Why Coca-Cola and Pepsi are so similar.
• Why Kellogg’s and Post both have purple raisin bran boxes.

11. Commitment Problems
• In many of the games we’ve looked at players cannot achieve
the desired outcome because of a commitment problem—
that is they cannot make credible threats or promises about
their future actions.
• Sometimes, it’s possible to adopt commitment devices
‒ Omerta: anyone who testifies
against a fellow mob member is
killed.
‒ Legally binding contracts
‒ Commissions to salespeople

12. Commitment Problems
• Sometimes we want to commit ourselves . . .
– Bring a fixed amount of cash when you go out.
– Leave your laptop at work so you don’t work from home.
– Brush your teeth to avoid snacking later.
– Cut up your credit cards.

13. Commitment Problems
• Sometimes psychological incentives can solve commitment
problems
– Guilt
– Sympathy towards others

14. Stranger
A
Give $
Keep
the $
Don’t
Give $
Buy
Tacos
-20 for you
20 for the stranger
5 for you
10 for stranger
0 for you
0 for stranger
You’re hungry but too busy to go buy lunch, so you
give a stranger $20 to go buy you two fish tacos
(which you value at $25).
A. Give, Keep
B. Give, Buy
C. Don’t give

15. Stranger
A
Give $
Keep
the $
Don’t
Give $
Buy
Tacos
-20 for you
-10 for your friend
5 for you
10 for your friend
0 for you
0 for your friend
You’re hungry but too busy to go buy lunch, so you
give your best friend $20 to go buy you two fish tacos
(which you value at $25).
A. Give, Keep
B. Give, Buy
C. Don’t Give

16. Lesson
• Having a trustworthy trading partner can make both parties
better off.
• The hard part is identifying people who you can trust.
• Reputation matters.

17. Splitting a cake
Donnie
Marie
50/50
>.5
Big/Small
<.5
0.5 (D)
0.5 (M)
<0.5 (D)
>0.5 (M)
>0.5 (D)
<0.5 (M)