Risk Preferences
A Microeconomic Systems
Perspective
Experimenter would like to
improve performance.
Performance
Environment (E)
Outcomes (Q)
Institution (I)
Governs
Computes
Behavior
bi: E X I  M
i = 1 , …, n
Messages
(M)
Experimenter would like to predict behavior.
Daniel Kahneman
Making Decisions
Decision Trees
B
t
time
A
t+1
Evaluating the Consequences of
Uncertain Decisions
p
B
t
1-p
A
time
q
1-q
t+1
Example Use of Decision Theory
Yacht Company: Inventory Decision
100
Good
.6
.4
170
Bad
Profit = 350
Good
.6
160
.4
Bad
Profit = 200
Profit = -100
170
50
Profit = 100
Decision Tree
Small Yacht Company
But What About Utility
?
100
50
?
Good
.6
.4
Bad
U(350)
Good
.6
.4
Bad
U(200)
U(-100)
U(100)
When would the yacht company owner pick down?
How are Virtual Worlds different
From the Yacht owner problem?
How are Virtual Worlds different
From the Yacht owner problem?
Price of Yacht:
Cost of Yacht:
Unit Profit:
85K
50K
35K
Avoidable FC:
Fixed Cost:
50K
100K
How are Virtual Worlds different
From the Yacht owner problem?
Price of Yacht:
Cost of Yacht:
Unit Profit:
85K
50K
35K
Price of virtual good: 100L
Cost of virtual good:
0L
Unit Profit:
100L
Avoidable FC:
Fixed Cost:
50K
100K
Avoidable Fixed Cost:
Marketing: 5000L
50 Hours*: 625,000L
* Hours to make first unit x opportunity cost
$50/hour x 250 L to $.
What matters is opportunity cost,
size of the market,
and willingness to buy
Price of virtual good: 100L
Cost of virtual good:
0L
Unit Profit:
100L
Price of virtual good: 100L
Cost of virtual good:
0L
Unit Profit:
100L
Avoidable Fixed Cost:
Marketing: 5000L
50 Hours*: 625,000L
Avoidable Fixed Cost:
Marketing:
5000L
50 Hours**: 125,000L
*$50 an hour
**$10 an hour
What happens if someone enjoys building?
A Simple Analytic
Price of virtual good: 100L
Cost of virtual good:
0L
Unit Profit:
100L
Avoidable Fixed Cost:
Marketing: 5000L
50 Hours*: 625,000L
(Venture) = E(n) x p – 5000 – C(H)
Where C(H) = [o – v]H, o = market opportunity cost of time,
and v = fun value of time.
If v > o will the creator market his or her product?
Indirect Utility Function
V(p1, p2, m) = U[h1(p1, p2, m), h2(p1, p2, m)]
and holding prices constant we have,
Utility
V/m > 0.
U(m|p1, p2)
V(m2)
V(m1)
Money
m1
m2
Utility of Money
Concave Function
Utility
U(m)
U(m2)
U(m1)
Money
m1
m2
Adding Uncertainty
Expected Value (EV)
Utility
p
m1
g
U(m)
Money
m1
EV
m2
EV = p m1 + (1-p) m2
1-p
m2
Expected Utility
EU(g)
Utility
p
m1
g
U(m)
EU(g)
EU(g) = p U(m1) + (1-p) U(m2)
Money
m1
EV
m2
EV = p m1 + (1-p) m2
1-p
m2
Effect of Increasing Variance
Risk Aversion
Utility
p
m1
g
U(m)
EU(g)
EU(f)
1-p
m2
p
M1
f
1-p
Money
M1
m1
EV
m2
M2
M2
Calculating the Certainty Equivalent
Utility
U(CE) = EU(g)
p
m1
g
U(m)
EU(g)
1-p
m2
Notice for risk aversion
CE < EV.
Money
m1 CE
EV
m2
Risk Premium: RP = EV - CE
Notice for risk aversion
RP > 0.
Calculating the Certainty Equivalent
Utility
U(CE) = EU(g)
p
m1
g
U(m)
EU(g)
1-p
m2
Notice for risk aversion
CE < EV.
Money
m1 CE
EV
m2
Risk Premium: RP = EV - CE
Notice for risk aversion
RP > 0.
Risk Sharing
Can people trade risk?
Risk Sharing
Can people trade risk?
Insurance Markets
Maintain a portfolio of uncorrelated risks
allows the insurance company to be risk
neutral.
But consumers are willing to pay their
RP to the insurance company to have the
insurance company take their risk.
Competition determines the price,
0 < p < RP
Risk Sharing
Can the owner of the Yacht
company manage her risk?
yes/no/how
Can the owner of a Virtual World
product manage her risk?
yes/no/how
Early Traders and Risk Sharing
• Example: trader making a shipment
– U(x) = sqrt(x) (risk aversion)
– X2 = 900,000 (shipment arrives)
– P2 = .9
– X1 = 0 (shipment is stolen)
– P1 = .1
• Trader’s decision is a gamble
– G = (0, .1, 900,000, .9)
– EU(G) = .9 sqrt(900,000) + .1 sqrt(0) = 854
Each Trader Faces the Same Gamble
Trader 1’s Gamble
0
.1
G1
.9
Trader 2’s Gamble
0
.1
G2
900K
.9
900K
Early Traders and Risk Sharing
• What if two traders contract?
– Each sends half of his cargo on the other’s ship
• Chance of both shipments being stolen: .1*.1 = .01
• Chance of shipment one being stolen: .1*.9 = .09
• Chance of shipment two being stolen: .9*.1 = .09
• Chance of two successful shipments: .9*.9 = .81
50% shares of venture
Traders’ Subgamble
Aggregate Gamble
.01
G
0
.09
.09
.01
900K
900K
GJ
0
.09
.09
450K
450K
.81
.81
1800K
900K
50% shares of venture
Traders’ Subgamble
Aggregate Gamble
.01
G
0
.09
.09
.01
900K
900K
GJ
0
.09
.09
450K
450K
.81
.81
1800K
900K
New gamble (J) with three potential outcomes
J = (0, .01, 450,000, .18, 900,000, .81)
EU(J) = .18 sqrt(450,000) + .81 sqrt(900,000) = 889
Traders Better Off Risk Sharing
• EU trading individually = 854
• EU w/risk sharing contract = 889
Both traders are better off
–Chance of getting $900,000
decreases from 90% to 81%
–Chance of getting 0 decreases from
10% to 1%
Measuring Risk Preferences
Risk Aversion and Incentive Effects
Charles A. Holt and Susan K. Laury
The American Economic Review
Vol. 92, No. 5 (Dec., 2002), pp. 16441655
Decision Tasks
Decision
Option A
1
400 if throw of die is 1
500 if throw of die is 2-10
400 if throw of die is 1-2
500 if throw of die is 3-10
400 if throw of die is 1-3
500 if throw of die is 4-10
400 if throw of die is 1-4
500 if throw of die is 5-10
400 if throw of die is 1-5
500 if throw of die is 6-10
400 if throw of die is 1-6
500 if throw of die is 7-10
400 if throw of die is 1-7
500 if throw of die is 8-10
400 if throw of die is 1-8
500 if throw of die is 9-10
400 if throw of die is 1-9
500 if throw of die is 10
400 if throw of die is 1-10
2
3
4
5
6
7
8
9
10
Option B
960 if throw of die is 1
25 if throw of die is 2-10
960 if throw of die is 1-2
25 if throw of die is 3-10
960 if throw of die is 1-3
25 if throw of die is 4-10
960 if throw of die is 1-4
25 if throw of die is 5-10
960 if throw of die is 1-5
25 if throw of die is 6-10
960 if throw of die is 1-6
25 if throw of die is 7-10
960 if throw of die is 1-7
25 if throw of die is 8-10
960 if throw of die is 1-8
25 if throw of die is 9-10
960 if throw of die is 1-9
25 if throw of die is 10
960 if throw of die is 1-10
Your Choice
(Circle A or B)
A
B
A
B
A
B
A
EVA EVB
490
118.5
480
202
470
305.5
B
460
399
A
B
450
492.5
A
B
440
586
A
B
430
679.5
A
B
420
773
A
B
410
866.5
A
B
400
960
Risk Neutral Prediction
% choice of A
RN
1
0.8
0.6
RN
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
Decision
Making Risky Decisions for Others
Data From The Experiment
Decision Task for Judges’ Experiment
Decision
1
2
3
4
5
6
7
8
9
10
Option A
$12 if throw of die is 1
$15 if throw of die is 210
$12 if throw of die is 12 $15 if throw of die is
3-10
$12 if throw of die is 13 $15 if throw of die is
4-10
$12 if throw of die is 14 $15 if throw of die is
5-10
$12 if throw of die is 15 $15 if throw of die is
6-10
$12 if throw of die is 16 $15 if throw of die is
7-10
$12 if throw of die is 17 $15 if throw of die is
8-10
$12 if throw of die is 18 $15 if throw of die is
9-10
$12 if throw of die is 19 $15 if throw of die is
10
$12 if throw of die is 1-10
Option B
Your Choice
(Circle A or B)
EVA
EVB
$29 if throw of die is 1
$1 if throw of die is 2-10
A
B
14.70 3.80
$29 if throw of die is 1-2
$1 if throw of die is 3-10
A
B
14.40 6.60
$29 if throw of die is 1-3
$1 if throw of die is 4-10
A
B
14.10
$29 if throw of die is 1-4
$1 if throw of die is 5-10
A
B
13.80 12.20
$29 if throw of die is 1-5
$1 if throw of die is 6-10
A
B
13.50 15.00
$29 if throw of die is 1-6
$1 if throw of die is 7-10
A
B
13.20 17.80
$29 if throw of die is 1-7
$1 if throw of die is 8-10
A
B
12.90 20.60
$29 if throw of die is 1-8
$1 if throw of die is 9-10
A
B
12.60 23.40
$29 if throw of die is 1-9
$1 if throw of die is 10
A
B
12.30 26.20
$29 if throw of die is 1-10
A
B
12.00 29.00
9.40
Judges’ Experiment (in progress)
Fraction Choosing Safe Option A
1.2
1
0.8
RN
0.6
Self
Other
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
Thank You