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Humans regularly pursue activities characterized by dramatic success or failure outcomes where, critically, the chances of success depend on the time invested working towards it. How should peo- ple allocate time between such make-or-break challenges and safe alternatives, where rewards are more predictable (e.g., linear) functions of performance? We present a formal framework for studying time allocation between these two types of activities, and we explore optimal behavior in both one-shot and dynamic versions of the problem. In the one-shot version, we illustrate striking discontinuities in the optimal time allocation policy as we gradually change the parameters of the decision-making problem. In the dynamic version, we formulate the optimal strategy, defined by a giving-up threshold, which adap- tively dictates when people should abandon the make-or-break goal; we also show that this strategy is computationally unattainable for humans. We then pit this strategy against a boundedly rational alter- native using a myopic giving-up threshold that is far simpler to compute, as well as against a simple heuristic that only decides whether or not to start pursuing the goal and never gives up. Comparing strategies across environments, we investigate the cost and behavioral implications of sidestepping the computational burden of full rationality.
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