People Missallocate Risk-Reduction Investments in Decisions Under Extinction Risk

Many real-world decisions involve small probabilities of irrecoverable loss, where failure eliminates the possibility of making future decisions. Such decisions under extinction risk differ fundamentally from standard risky choice. We study how people allocate resources to reduce extinction risks. Participants play 100 trials with variable extinction risks of 2.5%, 5%, and 10%. If a participant draws the extinction outcome, they lose all accumulated bonus payment and are precluded from further earnings. Participants can reduce extinction risk by investing earnings: for every £0.02 invested, the extinction risk in the current trial is halved. We use dynamic programming to derive the optimal investment decision for each choice and compare it with participants' investments. Our results show that participants overinvest in reducing small risks, underinvest in reducing larger risks, and fail to adjust their investment appropriately across trials, leading them to go extinct at a higher rate compared to the optimal strategy.