Time Horizons in
Interdependent Security
David Hardisty, Howard Kunreuther,
David Krantz, & Poonam Arora
Columbia University
International Conference on Social Dilemmas
Kyoto, Japan
August 24, 2009
Co-Authors
Howard Kunreuther
Dave Krantz
Poonam Arora
NSF Grants SES-0345840 & SES-0820496
IDS Background
• Interdependent Security (IDS) is a social
dilemma with stochastic losses
examples:
• border security
• pest/disease control
• risky investment
Thank You
ICSD 2009 Organizing Committee
•
•
•
•
•
Satoshi Fujii
Toshio Yamagishi
Tsuyoshi Hatori
Akira Kikuchi
Haruna Suzuki
Previous Findings on IDS
• Individuals cooperate less in IDS than in a
typical repeated PD (Kunreuther et al, in press)
• However groups cooperate more in IDS (Gong,
Baron & Kunreuther, in preparation)
Group and Uncertainty Interaction
Deterministic
Game
Proportion of
Investing
100%
Stochastic
Game
75%
50%
25%
0%
1
Group
2
Individual
Player Type
Research Motivation (1)
• Previous studies used probabilities of 20%
to 80%
• Real life risks are often much lower
Research Motivation (2)
• In real life, players often precommit their
strategy (whether to invest in protection)
for several years in advance at a time
• example: CO2 reductions
Research Motivation (2)
• Normally, greater delay is associated with
increased uncertainty
• example: $10 promised today or in 20
years
• However, with repeated low probability
events, increasing time horizon may
increase subjective probability
• example: chance of fire today or in the
next 20 years
Study 1
Question 1: Do previous findings of low
(~30%) cooperation under uncertainty
hold with low probabilities? Or will it be
even lower?
Question 2: Does precommitment raise
investment rates?
IDS instructions (pg 1)
Scenario: Imagine you are an investor in Indonesia
and you have a risky joint venture that earns
8,500 Rp per year. However, there is a small
chance that you and/or your counterpart will
suffer a loss of 40,000 Rp in a given year. You
have the option to pay 1,400 Rp for a safety
measure each year to protect against the
possible loss. However, you will only be fully
protected if both you and your counterpart invest
in protection. The loss has an equal chance of
happening each year, regardless of whether it
occurred in the previous year.
IDS payoff matrix
Your Counterpart
You INVEST
NOT
INVEST
INVEST
NOT INVEST
- You definitely lose 1,400
Rp, and have a 0% chance
of the large loss occurring.
- You definitely lose 1,400 Rp and
have a 1% chance of losing an
additional 40,000 Rp.
- Your counterpart definitely
loses 1,400 Rp, and has a
0% chance of the large loss
occurring.
- Your counterpart has a 3%
chance of losing 40,000 Rp and a
97% chance of losing 0 Rp.
- You have a 3% chance of
losing 40,000 Rp and a 97%
chance of losing 0 Rp.
- You have a 4% chance of losing
40,000 Rp and a 96% chance of
losing 0 Rp.
- Your counterpart definitely
loses 1,400 Rp and has a
1% chance of losing an
additional 40,000 Rp.
- Your counterpart has a 4%
chance of losing 40,000 Rp and a
96% chance of losing 0 Rp.
PD payoff matrix
Your Counterpart
INVEST
NOT INVEST
You INVEST
- You lose 1,400 Rp.
- Your counterpart loses
1,400 Rp.
- You lose 1,800 Rp.
- Your counterpart loses 1,200 Rp.
NOT
INVEST
- You lose 1,200 Rp.
- Your counterpart loses
1,800 Rp.
- You lose 1,600 Rp.
- Your counterpart loses 1,600 Rp.
IDS: Choices
Will you invest in protection this year?
INVEST | NOT INVEST
Do you think your counterpart will invest in protection this year?
DEFINITELY | PROBABLY | PROBABLY NOT | DEFINITELY NOT
Precommitted Condition
Will you invest in protection in year 1?
INVEST | NOT INVEST
Do you think your counterpart will invest in protection in year 1?
DEFINITELY | PROBABLY | PROBABLY NOT | DEFINITELY NOT
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Will you invest in protection in year 2?
INVEST | NOT INVEST
Do you think your counterpart will invest in protection in year 2?
DEFINITELY | PROBABLY | PROBABLY NOT | DEFINITELY NOT
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[...]
Will you invest in protection in year 20?
INVEST | NOT INVEST
Do you think your counterpart will invest in protection in year 20?
DEFINITELY | PROBABLY | PROBABLY NOT | DEFINITELY NOT
Feedback
Year 1 Results
Your choice: INVEST
Your counterpart's choice: NOT INVEST
The random number was: 88
This Means
For you, the large loss: did not occur
For your counterpart, the large loss: did not occur
Result: You lost 1,400 Rp, and your counterpart lost 0 Rp
Design Details
• participants played blocks of 20 rounds
(“years”) with an anonymous partner
• 4 blocks total
• random pairing before each block
• 1 block paid out for real money
• all manipulations between subject, 30
subjects per group
PD vs IDS
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
0.5
PD rep
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
PD vs IDS
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
0.5
PD rep
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
PD vs IDS
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
0.5
PD rep
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 1
• Uncertainty lowers cooperation between
individuals playing loss framed dilemma
• Why?
- Perhaps uncertainty makes players more
greedy (Johansson & Svedsater,
yesterday)
- Perhaps uncertainty transforms the game
from a social dilemma to a game of
chance
IDS: repeated vs precommitted
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
PD rep
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
IDS: repeated vs precommitted
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
PD rep
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 2
• Under uncertainty, precommitment raises
cooperation
• Why? Perhaps precommitment raises
subjective probability of the loss
Precommitted Participants Estimated
Higher Cumulative Probability
Interesting results, but a major
confound:
Feedback
Study 2
Question: Do individuals playing a
(non-dilemma) solo game invest
more often when precommitting?
Solo payoff matrix
INVEST
- You definitely lose 1,400 Rp, and have a 0% chance of
the large loss occurring.
NOT INVEST
- You have a 4% chance of losing 40,000 Rp and a 96%
chance of losing 0 Rp.
IDS repeated vs Solo repeated
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
Solo rep
Solo pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
IDS repeated vs Solo repeated
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
Solo rep
Solo pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 3
• IDS players are mostly playing a game of
chance, showing risk-seeking for losses
Support 3
Solo: repeated vs precommited
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
Solo rep
Solo pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Solo: repeated vs precommited
1
0.9
Investment Proportion
0.8
0.7
0.6
IDS rep
IDS pre
Solo rep
Solo pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 4
• Precommitment raises investment rates by
individuals
• Why? Perhaps subjective probability is
increased
How else can we improve
investment under uncertainty?
• Perhaps environmental framing can
highlight social goals and raise investment
rates
• However, earlier results are mixed
Study 3
Question: Will environmental
framing will increase
investment rates?
IDS environmental instructions
Scenario: Imagine you are a farmer in Indonesia. You get
an annual yield of 8,500 Rupiah (Rp) from your potato
crops. Both you and a neighboring farmer use the
pesticide Aldicarb on your potato crops. However, there
is a small risk of groundwater contamination each year
from this pesticide, which is toxic. If contamination
occurs, you and/or your neighboring farmer will suffer a
loss of 40,000 Rp, to pay for groundwater cleanup. You
have the option to switch to a more expensive, though
safer, pesticide, at the cost of 1,400 Rp annually, to
avoid groundwater contamination. However, you will only
be fully protected if both you and your counterpart invest
in the safer pesticide. The groundwater contamination
has an equal chance of happening each year, regardless
of whether it occurred in the previous year.
IDS environmental payoff matrix
Your Counterpart
You
INVEST
INVEST
NOT INVEST
- You definitely lose 1,400 Rp,
and have a 0% chance of
groundwater contamination.
- You definitely lose 1,400 Rp and
have a 1% chance of groundwater
contamination occuring and losing an
additional 40,000 Rp.
- Your counterpart definitely
loses 1,400 Rp, and has a 0%
chance of groundwater
contamination.
NOT
INVEST
- Your counterpart has a 3% chance
of losing 40,000 Rp due to
groundwater contamination and a
97% chance of losing 0 Rp.
- You have a 3% chance of
losing 40,000 Rp due to
groundwater contamination and
a 97% chance of losing 0 Rp.
- You have a 4% chance of
groundwater contamination occurring
and losing 40,000 Rp and a 96%
chance of losing 0 Rp.
- Your counterpart definitely
loses 1,400 Rp and has a 1%
chance of groundwater
contamination occuring and
losing an additional 40,000 Rp.
- Your counterpart has a 4% chance
of groundwater contamination
occurring and losing 40,000 Rp and a
96% chance of losing 0 Rp.
IDS Environmental: Choices
Will you invest in the safer pesticide this year?
INVEST | NOT INVEST
Do you think your counterpart will invest in the safer pesticide this
year?
DEFINITELY | PROBABLY | PROBABLY NOT | DEFINITELY NOT
Feedback
Year 1 Results
Your choice: INVEST
Your counterpart's choice: NOT INVEST
The random number was: 88
This Means
For you, groundwater contamination: did not occur
For your counterpart, groundwater contamination : did
not occur
Result: You lost 1,400 Rp, and your counterpart lost 0 Rp
Environmental Frame Results
1
0.9
Investment Proportion
0.8
0.7
IDS rep
IDS pre
IDS rep E
IDS pre E
0.6
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Environmental Frame Results
1
0.9
Investment Proportion
0.8
0.7
IDS rep
IDS pre
IDS rep E
IDS pre E
0.6
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Environmental Frame Results
1
0.9
Investment Proportion
0.8
0.7
IDS rep
IDS pre
IDS rep E
IDS pre E
0.6
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 5
• Environmental framing may not have a
significant effect on investment rates
Study 4
Question: How does precommitment
affect investment rates in a
deterministic prisoners dilemma
IDD payoff matrix
Your Counterpart
INVEST
NOT INVEST
You INVEST
- You lose 1,400 Rp.
- Your counterpart loses
1,400 Rp.
- You lose 1,800 Rp.
- Your counterpart loses 1,200 Rp.
NOT
INVEST
- You lose 1,200 Rp.
- Your counterpart loses
1,800 Rp.
- You lose 1,600 Rp.
- Your counterpart loses 1,600 Rp.
PD: Repeated vs Precommitted
1
0.9
Investment Proportion
0.8
0.7
0.6
PD rep
PD pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
PD: Repeated vs Precommitted
1
0.9
Investment Proportion
0.8
0.7
0.6
PD rep
PD pre
0.5
0.4
0.3
0.2
0.1
0
Block 1
Block 2
Block 3
Block 4
Conclusion 6
• Precommitment reduces investment rates
in deterministic social dilemmas
• Why? Perhaps individuals realize there is
no opportunity for reciprocity and are
worried about being a sucker
Summary
• Precommitment lowers cooperation in
regular prisoner’s dilemma, but raises it in
interdependent security situations
• Why? In IDS, precommitment raises
subjective probability of loss, but in the
deterministic case it removes the
possibility of reciprocity
Thank You!
References
Gong, M. J. Baron and H. Kunreuther (2008).
Group Cooperation under Uncertainty. Wharton
Risk Center Working Paper # 2008-11-24
Kunreuther, H., G. Silvasi, E. Bradlow, and D.
Small (in press). Deterministic and Stochastic
Prisoner's Dilemma Games: Experiments in
Interdependent Security. Judgment and
Decision Making.
Xiao, Erte & Kunreuther, H. (in preparation).
Punishment and Cooperation in Stochastic
Social Dilemmas.
Questions
• Do you believe the risk perception story?
• What new conditions would be most
interesting? All-or-nothing
precommitment? Group play? Change the
payoffs (so non-investment dominates)?
• What journals do you recommend
publishing in?
• What are the biggest holes in this story?
What about individual
differences?
Comprehensive Health Insurance
Gender
Gender
First-Round Comparison
Overall Comparison
20-Round Profile
80 Round Profile
What did people say?
IDS - Repeated
• The probability of loosing was too low so I didn't decide to invest.
• For the most part, it seemed better NOT to invest than to invest. I
found that the initial 1-5 years influenced how I invested in the
remaining 15 years. So if I mainly did NOT invest the first 5 years,
then I didn't invest for the remaining 15 years. I also found that my
partner followed how I invested if I had no losses.
• I chose not to invest dut to low probality of loss
• It was a little intimidating, but after awhile an understanding occurred
between myself and my partner and we flowed fairly well over the
years.
• I chose to invest in the beginning so I wouldn't end up with negative
numbers. Afterwards, I chose not to invest because I figured the
chances of losing 40,000 were small, and even if I lost the money
once, I would probably not lose it again in the 20 year span.
IDS - Precommitted
• I chose to invest almost all 20 times except for one or 2 years to
make an extra bonus
• An interesting game where I can observe that some people do take
risks. I chose to invest in every year and every scenario since
statistically it makes more sense to invest in protection. The loss is
big compared to the amount spent on protection and there is an
average of more than one occurrence of loss in a 20 year period
even if only one person invests.
• I invested too many times the first round, and when I saw that my
partner rarely invested and suffered little losses, I invested less as
well by the next round. I felt rather smug when he/she lost 40k while
I invested-- but I thought it was interesting that I invested a lot more
often than most of my counterparts.
• Initially I was just playing it safe, and then for the 2 later rounds I
pretty much went with the Nash Equilibrium choice of Not Investing.
Solo - Repeated
• At first, it seemed as though investing would be a good
idea. After the second round, I realized that not investing
would probably give a better payout because the
chances of actually suffering a loss was so slim.
• I mainly choose to not invest because there was only a
4% chance of losing 40000 Rp. But then every 4 or 5
turns, I would randomly decide to invest in protection.
Now that I think about it, even if I hadn't gone with
investing at all, the outcome may have been the same or
maybe even better.
• I would invest at points where I thought that I was happy
enough with my cumulative gains that I didn't want to risk
losing what I had already gained.
Solo - Precommitted
• It's obvious safer to invest, and the investment totally
worth that. Even if you invest for 20 years, the cost is
lower than one large loss which might happen every year.
However, as there was no large loss happened in the
first session, I therefore chose to take some risks in
following sessions.
• The potential loss from investing every time seemed less
than from not investing more often where even one bad
year could produce less income.
• 40000 Rp possible loss * 4% chance = 1600 Rp loss
expected. So in general it's worth it to invest. However,
given the low likelihood, it might be worth it to take a risk
& skip some years.
Why Groups Cooperate More
than Individuals in SPD
- Safety Oriented to Avoid Guilt and Blame
• People take less risk when their decisions affect
others (Charness and Jackson 2008)
• In DPD
– Defection is always better off
– No ex post guilt or blame
• In SPD
– Defection has a higher expected payoff, but also a
higher probability of suffering a loss.
– If a large loss follows defection ex post guilt and ex
post blame for the one who suggested defection
– Group members favor safety-oriented strategy
(cooperation) to avoid ex post guilt and blame
Reversed discontinuity effect
Why Groups Cooperate More than Individuals in SPD
-Social Pressure to Conform to Certain Norms
• Three norms are most relevant in PD games: Being
pro-group, Being smart, and Being nice
• Similar to the group morality and individual morality
argument (Cohen 2006; Pinter 2007)
• In DPD
– Both pro-group (group morality) and smart norm
clearly indicate defection
– Niceness (individual morality) is clouded
• In SPD
– Unclear what strategy is pro-group and smart
– Being nice is socially desirable and more salient than
in DPD.