1. 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 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. 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: CO 2 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 Methods Contact: djh2117@columbia.edu, http://davidhardisty.info Support: NSF grants SES-0345840 and SES-0820496 Abstract 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 Introduction Results References 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. Your Counterpart INVESTNOT INVEST YouINVEST- You definitely lose 1,400 Rp, and have a 0% chance of the large loss occurring. - Your counterpart definitely loses 1,400 Rp, and has 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 has a 3% chance of losing 40,000 Rp and a 97% chance of losing 0 Rp. NOT INVEST - You have a 3% chance of losing 40,000 Rp and a 97% chance of losing 0 Rp. - Your counterpart definitely loses 1,400 Rp and has a 1% chance of losing an additional 40,000 Rp. - You have a 4% chance of losing 40,000 Rp and a 96% chance of losing 0 Rp. - Your counterpart has a 4% chance of losing 40,000 Rp and a 96% chance of losing 0 Rp. 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. Your Counterpart INVESTNOT INVEST YouINVEST- 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. Prisoner’s Dilemma (PD) Solo Game Interdependent Security (IDS) Payoff Matrix Replicating previous research, investment rates were lower in IDS than in PD. Confirming H1, investment rates in the IDS game increased with precommitment: Confirming H2, solo players showed the same pattern as IDS players: In the (deterministic) prisoner’s dilemma, precommitment lowered investment: