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Time Horizons in Interdependent Security David J. Hardisty, Howard Kunreuther, David H. Krantz, & Poonam Arora Columbia University & University of Pennsylvania. Confirming H2, solo players showed the same pattern as IDS players:. Abstract. Methods.

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Participants played 4 blocks of 20 rounds randomly assigned to a new counterpart each block

Time Horizons in Interdependent SecurityDavid J. Hardisty, Howard Kunreuther, David H. Krantz, & Poonam AroraColumbia University & University of Pennsylvania

Confirming H2, solo players showed the same pattern as IDS players:



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.

  • 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

Interdependent Security (IDS) Payoff Matrix

In the (deterministic) prisoner’s dilemma, precommitment lowered investment:


  • 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

  • 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

  • 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

Solo Game

Prisoner’s Dilemma (PD)


  • 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


Replicating previous research, investment rates were lower in IDS than in PD. Confirming H1, investment rates in the IDS game increased with precommitment:


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.

Contact: djh2117@columbia.edu, http://davidhardisty.info

Support: NSF grants SES-0345840 and SES-0820496