Strategic Business Program
Business, Government,
Society: Insights from
Experiments
Day 2
1
Today’s plan




Some
Some
Some
Some
wicked problems
experiments
time for a break
game theory
2
Wicked problem #1

What’s the best way to get to Long
Beach, CA?


Always?
Why/why not?
3
Los Angeles and vicinity, 1959
Source: http://www.cahighways.org/maps/1959rmn.jpg, from 1959 Rand McNalley Road Atlas
and Radio Guide, currently out of print. The map is found on pages 58-59.
4
A more
current
Los
Angeles
area
freeway
grid
Highway
91
Sepulveda
Pass
Picture source: https://upload.wikimedia.org/wikipedia/en/a/aa/SocalfreewaysystemWIKI.jpg, by Mike Smith
5
What has happened?

When freeways were built, fewer
people traveled long distances to work
Building the San
Diego Freeway
through
Sepulveda Pass,
1961
Source: Los Angeles Times Photographic Archive.
Department of Special Collections, Charles E. Young
Research Library, UCLA. Accessed from
https://www.kcet.org/shows/lost-la/before-thecarmageddon-a-photographic-look-at-theconstruction-of-5-socal-freeways
6
Photo from
https://en.wikipedia.org/wiki/Sepulveda_Pass,
by Cbl62
Today


According to the Los Angeles Metro
website (https://www.metro.net/projects/sfv405/), concepts for improving this oftencongested corridor include building a
tunnel under the pass
According to Los Angeles Magazine in May
2015 (http://www.lamag.com/driver/new-metro-ceo-bullish-on-tunnel-under405/), such a tunnel could cost $20 billion
7
Another wicked problem

Welfare/unemployment benefits



Many people want to have a social safety
net
However, these payments may discourage
some people from seeking work
How do we analyze these problems?


Natural experiments
Gather data from government programs
8
Some experiments


Listen for directions
We will analyze these experiments later on
9
Up next

The route choice experiment




Analysis
Results of the lowest unique positive
integer (LUPI) game
Break
Some game theory
10
A Quick Introduction to
Game Theory
The fundamentals of game theory
Nash equilibrium
Classic examples
11
Introduction to Game Theory



We can look at market situations with two
players (typically firms)
Although we will look at situations where
each player can make only one of two
decisions, theory easily extends to three or
more decisions
Some classic examples (time permitting)
12
Three Elements in Every Game

Players



Two or more for most games that are
interesting
Strategies available to each player
Payoffs

Based on your decision(s) and the
decision(s) of other(s)
13
Game Theory: Payoff Matrix
Person 2
Action C
Person 1
Action D
Action A 10, 2
8, 3
Action B 12, 4
10, 1

A payoff
matrix
shows the
payout to
each
player,
given the
decision of
each
player
14
How do we interpret this box?
Person 2
Person
1
Action Action
C
D
Action 10, 2
8, 3
A
Action 12, 4 10, 1
B


The first number in
each box determines
the payout for
Person 1
The second number
determines the
payout for Person 2
15
How do we interpret this box?
Person 2
Person
1
Action Action
C
D
Action 10, 2
8, 3
A
Action 12, 4 10, 1
B

Example

If Person 1
chooses Action A
and Person 2
chooses Action D,
then Person 1
receives a payout
of 8 and Person 2
receives a payout
of 3
16
Core Principle: Equilibrium

The type of equilibrium we are looking
for here is called Nash equilibrium


Nash equilibrium: Each player’s strategy is
her/his best choice, given the choices of all
other players
Exactly one person deviating from a NE
strategy would result in the same payout
or lower payout for that person
17
How do we find Nash
equilibrium (NE)?



Step 1: Pretend you are one of the players
Step 2: Assume that your “opponent” picks a
particular action
Step 3: Determine your best strategy (strategies),
given your opponent’s action




Underline any best choice in the payoff matrix
Step 4: Repeat Steps 2 & 3 for any other opponent
strategies
Step 5: Repeat Steps 1 through 4 for the other
player
Step 6: Any entry with all numbers underlined is NE
18
Steps 1 and 2
Person 2
Action
C
Person
1
Action
A
10, 2
Action B 12, 4
Action D
8, 3
10, 1


Assume that
you are
Person 1
Given that
Person 2
chooses
Action C,
what is
Person 1’s
best choice?
19
Step 3
Person 2
Action
C
Person
1
Action
A
10, 2
Action B 12, 4

Action D
8, 3
10, 1

Underline
best payout,
given the
choice of the
other player
Choose
Action B,
since
12 > 10 
underline 12
20
Step 4
Person 2
Action C
Person
1
Action A 10, 2
Action
D

8, 3

Action B 12, 4
10, 1
Now
assume
that Person
2 chooses
Action D
Here,
10 > 8 
Choose and
underline
10
21
Step 5
Person 2
Action C

Action D

Person
1
Action
A
10, 2
8, 3


Action
B
12, 4
10, 1
Now,
assume you
are Person 2
If Person 1
chooses A
3>2
underline 3
If Person 1
chooses B

4>1
underline 4
22
Step 6
Person 2
Action C
Person
1

Action D
Action A 10, 2
8, 3
Action B 12, 4
10, 1
Which
box(es) have
underlines
under both
numbers?


Person 1
chooses B
and Person
2 chooses C
This is the
only NE
23
Double check our NE
Person 2
Action C
Person
1
Action A 10, 2

Action D
8, 3
What if
Person 1
deviates
from NE?


Action B 12, 4
10, 1
Could
choose A
and get 10
Person 1’s
payout is
lower by
deviating 
24
Double check our NE
Person 2
Action C
Person
1
Action A 10, 2

Action D
8, 3
What if
Person 2
deviates
from NE?


Action B 12, 4
10, 1
Could
choose D
and get 1
Person 2’s
payout is
lower by
deviating 
25
Dominant Strategy
Person 2
Action C
Person
1
Action A 10, 2

Action D
8, 3
A strategy is
dominant if that
choice is
definitely made
no matter what
the other
person chooses

Action B 12, 4
10, 1
Example:
Person 1 has a
dominant
strategy of
choosing B
26
New Example
Person 2
Yes
Person
1
No
Yes
20, 20
5, 10
No
10, 5
10, 10

Suppose in
this example
that two
people are
simultaneously
going to
decide on this
game
27
New Example
Person 2
Yes
Person
1
No
Yes
20, 20
5, 10
No
10, 5
10, 10

We will go
through the
same steps to
determine NE
28
Two NE Possible
Person 2
Yes
No


Person
1
Yes
20, 20
5, 10
No
10, 5
10, 10
(Yes, Yes) and
(No, No) are
both NE
Although (Yes,
Yes) is the more
efficient
outcome, we
have no way to
predict which
outcome will
actually occur
29
Two NE Possible

When there are multiple NE that are
possible, economic theory tells us little
about which outcome occurs with
certainty
30
Two NE Possible

Additional information or actions may
help to determine outcome

If people could act sequentially instead of
simultaneously, we could see that 20, 20
would occur in equilibrium
31
Sequential Decisions


Suppose that decisions can be made
sequentially
We can work backwards to determine
how people will behave


We will examine the last decision first and
then work toward the first decision
To do this, we will use a decision tree
32
Decision tree in a sequential
game: Person 1 chooses first
Person 1
chooses
yes
B
A
Person 1
chooses
no
C
Person 2
chooses
yes
20, 20
5, 10
Person 2
chooses no
Person 2
chooses
yes
10, 5
Person 2
chooses no
10, 10
33
Decision tree in a sequential
game: Person 1 chooses first
Person 1
chooses
yes
B
A
Person 1
chooses
no
C
Person 2
chooses
yes
20, 20

5, 10
Person 2
chooses no
Person 2
chooses
yes
10, 5
Person 2
chooses no
10, 10

Given point B,
Person 2 will
choose yes
(20 > 10)
Given point C,
Person 2 will
choose no
(10 > 5)
34
Decision tree in a sequential
game: Person 1 chooses first
Person 1
chooses
yes
B
A
Person 1
chooses
no
C
Person 2
chooses
yes
20, 20

5, 10
Person 2
chooses no
Person 2
chooses
yes
10, 5
Person 2
chooses no

If Person 1 is
rational, she will
ignore potential
choices that
Person 2 will not
make
Example: Person
2 will not choose
yes after Person 1
chooses no
10, 10
35
Decision tree in a sequential
game: Person 1 chooses first
Person 1
chooses
yes
B
A
Person 1
chooses
no
C
Person 2
chooses
yes
20, 20

5, 10
Person 2
chooses no
Person 2
chooses
yes

10, 5
Person 2
chooses no
10, 10

If Person 1 knows
that Person 2 is
rational, then she
will choose yes,
since 20 > 10
Person 2 makes a
decision from point
B, and he will
choose yes also
Payout: (20, 20)
36
Prisoner’s dilemma
Player 2
Yes
Player
1

No
Why is this
game called
prisoner’s
dilemma?

Yes
–1, –1
+3, –6
No
–6, +3
+1, +1
Think about a
pair of
criminals that
have a choice
of whether or
not to confess
to a crime
37
Prisoner’s dilemma
Player 2
Yes

No
What is the
NE?

Player
1
Yes
–1, –1
+3, –6
No
–6, +3
+1, +1
Let’s
underline
38
Prisoner’s dilemma
Player 2
Yes

No
What is the
NE?


Player
1
Yes
–1, –1
+3, –6

No
–6, +3
+1, +1
Let’s
underline
Each player
has a
dominant
strategy of
choosing Yes
However,
both players
get a better
payout if each
chooses No
39
Battle of the Sexes
Player 2
Bar

Play
Bar +3, +1 +0, +0
Player 1
Play +0, +0 +1, +3

Two people plan a date,
and each knows that
the date is either at the
bar or a play

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)
40
Battle of the Sexes:
Other things to note
Player 2
Bar
Player 1

Play
Bar +3, +1 +0, +0
Play +0, +0 +1, +3


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
41
Battle of the Sexes
Player 2
Bar
Player 1

Play
Bar +3, +1 +0, +0
Play +0, +0 +1, +3
Two NE



(Bar, Bar)
(Play, Play)
As in cases before
when there are
multiple NE, we
cannot determine
which outcome will
actually occur
42
Battle of the Sexes
Player 2
Bar
Player 1

Play
Bar +3, +1 +0, +0
Play +0, +0 +1, +3
Battle of the Sexes
is known as a
coordination game

Both get a positive
payout if they show
up to the same place
43
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”
44
Chicken
Player 2
Player 1

Swerve
Straight
Swerve
+0, +0
–1, +1
Straight
+1, –1
–10, –10
Next step: Underline as before
45
Chicken
Player 2
Player 1

Swerve
Straight
Swerve
+0, +0
–1, +1
Straight
+1, –1
–10, –10
Notice there are 2 NE


One player swerves and the other goes straight
This game is sometimes referred to as an “anticoordination” game

NE results from each player making a different decision
46
Matching pennies
Player 2
Heads
Player
1
Tails
Heads +1, –1 –1, +1
Tails


–1, +1 +1, –1


Two players each
choose Heads or
Tails
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
47
Matching pennies
Player 2
Heads
Player
1
Tails
Heads +1, –1 –1, +1
Tails

–1, +1 +1, –1

A characteristic of
zero-sum games

Whenever I win, the
other player must
lose
Underlining shows
no NE
48
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
49
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
50
Subordinate Pig/Dominant Pig

Who do you think will get more food in
equilibrium?

Who thinks

Who thinks
?
?
51
Subordinate Pig/Dominant Pig

subordinate pig
dominant pig

Yes
No
Yes
3, 7
–1, 12
No
10, 1
0, 0
The numbers on the
previous slide translate to
the payoff matrix seen
Next:
Underline test
52
Subordinate Pig/Dominant Pig

dominant pig
subordinate pig
Yes
No
In Nash equilibrium, the
dominant pig always gets the
lower payout

Yes
3, 7
–1, 12
No
10, 1
0, 0



Exactly 1 NE

The dominant
pig presses lever
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
53
Do people always play as
Nash equilibrium predicts?

No


Many papers have shown that people often
are not selfish
Norms are often established to make sure
that people are encouraged to act in the
best interest of society
54
LUPI


Lowest unique positive integer game
The winner is the person that meets the
following criteria


Exactly one person picked the number
There is no smaller number in which
exactly one person picked that number
55
LUPI

Example with 20 participants






0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 8,
10, 50, 99, 100
0 does not win (not positive)
1 does not win (six people guessed this)
2 does not win (two people guessed this)
3 does not win (two people guessed this)
4 wins (exactly one person guessed this)
56
LUPI

NE is complicated

Many of you probably tried to figure out
what everyone else in the class guessed


Example: If you believe that everyone else will
pick 0, I should pick 1
Example: If you believe that everyone else will
pick 0 or 1 with probability ½, then I should
pick 2
57
Pick half the average

Rules:



Each person picks a number from 0 to 100
The person that picks the number closest
to half of the average wins
In case of a tie, the winners split the prize
58
Pick half the average


If you assume that each player picks a
number randomly between 0 and 100,
then I know the average is 50, and I
should pick 25
However, it would be irrational for
anyone to pick a number over 50, since
it cannot win  Should I pick a number
over 25?
59
Pick half the average

I can repeat this thinking an infinite
number of times to reach the NE


Everybody should pick 0
How many people picked…


0?
A number over 50?
60
Can you think of ways game theory
can be used in these games?
61