Time Horizons in
Interdependent Security
David J. Hardisty, Howard Kunreuther, David H. Krantz, & Poonam Arora
Columbia University & University of Pennsylvania
• Participants played 4 blocks of 20 rounds
• Randomly assigned to a new counterpart each block
• One block randomly paid out for real money
• 2 x 2 x 2 between-subjects design, 270 participants
Manipulations:
• Outcomes: stochastic (IDS) or deterministic (PD)
• Choices: repeated (ie, normal) or precommitted
• Number of players: pair or solo
INVEST
You
INVEST
• H1: IDS players will invest more often when
forced to precommit their choices
• H2: If the effect is due to uncertainty (rather than
strategy), solo players will do the same
- You definitely lose 1,400 Rp, and have a - You definitely lose 1,400 Rp and have a 1%
0% chance of the large loss occurring.
chance of losing an additional 40,000 Rp.
NOT
INVEST
- 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.
Prisoner’s Dilemma (PD)
Your Counterpart
INVEST
NOT INVEST
You INVEST - You lose 1,400 Rp. - You lose 1,800 Rp.
- Your counterpart
- Your counterpart loses
loses 1,400 Rp.
1,200 Rp.
Solo Game
INVEST
- You definitely lose 1,400
Rp, and have a 0%
chance of the large loss
occurring.
NOT INVEST
NOT
- You lose 1,200 Rp. - You lose 1,600 Rp.
INVEST - Your counterpart
- Your counterpart loses
loses 1,800 Rp.
1,600 Rp.
- You have a 4% chance of
losing 40,000 Rp and a
96% chance of losing 0
Rp.
Results
Replicating previous research, investment rates were
lower in IDS than in PD. Confirming H1, investment
rates in the IDS game increased with precommitment:
IDS repeated
IDS precommitted
PD repeated
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Solo repeated
Solo precommitted
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Block 2
In the (deterministic) prisoner’s dilemma,
precommitment lowered investment:
PD repeated
- Your counterpart definitely loses 1,400 - Your counterpart has a 3% chance of losing
Rp, and has a 0% chance of the large loss 40,000 Rp and a 97% chance of losing 0 Rp.
occurring.
Investment Proportion
• In real life, players often precommit their strategy
(whether to invest in protection) for several years in
advance at a time
• Example: CO2 reductions
• Normally, greater delay is associated with
increased uncertainty (Weber & Chapman, 2005)
• 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
Your Counterpart
NOT INVEST
IDS precommitted
1
Interdependent Security (IDS) Payoff Matrix
Introduction
• Interdependent Security (IDS) is a social dilemma
with stochastic losses (Kunreuther et al., 2009)
• Examples: border security, pest/disease control,
risky investment
• Investment rates in repeated IDS are normally
lower than those in a repeated prisoner’s dilemma
IDS repeated
PD precommitted
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Investment Proportion
Many real-world social dilemmas require
interdependent players to protect against a large
loss that has a low annual probability of occurring.
Examples include protecting against terrorism
(shared border security), protecting against disease
outbreak (think of bird flu), or climate change.
Decisions on whether to invest in protection may be
made year by year, or investment may be
precommitted for a number of years. Normally,
when an outcome is delayed, the subjective
uncertainty goes up. However, we hypothesized
and found that with recurring low probability events,
increasing the time horizon would increase the
subjective probability and thus (paradoxically)
increase investment rates.
Methods
Investment Proportion
Abstract
Confirming H2, solo players showed the same
pattern as IDS players:
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Discussion
• Precommitment lowers cooperation in regular
prisoner’s dilemma, but raises it in
interdependent security situations
• Why? In IDS, precommitment raises subjective
probability of loss
• Perhaps in the deterministic (PD) case,
precommitment removes the possibility of
reciprocity, and thereby lowers investment
References
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Kunreuther, H., Silvasi, G., Bradlow, E., & Small, D. (2009). Bayesian
analysis of deterministic and stochastic prisoner’s dilemma games.
Judgment and Decision Making, 4(5), 363-384.
Weber, B. J. & Chapman, G. B. (2005). The combined effects of risk
and time on choice: Does uncertainty eliminate the immediacy effect?
Does delay eliminate the certainty effect? Organizational Behavior
and Human Decision Processes, 96, 104-118.
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Contact: [email protected], http://davidhardisty.info
Support: NSF grants SES-0345840 and SES-0820496