Make-or-break: chasing risky goals or settling for safe rewards?

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.

人类常常投身于那些结果或喜或悲的活动，其中，成功的几率关键取决于为此投入的时间。人们在决定性挑战与安全选择之间如何分配时间，其中奖励是性能的更可预测的（例如，线性）函数？我们提出一个形式化的框架来研究这两种类型活动之间的时间分配，并探讨了该问题的单次和动态版本中的最优行为。在单次版本中，我们展示了当决策问题的参数逐渐变化时，最优时间分配策略中的显著不连续性。在动态版本中，我们制定了一个以放弃阈值定义的最优策略，该策略适应性地指示人们何时应放弃决定性目标；我们还表明，这一策略对于人类来说在计算上是不可实现的。随后，我们将这一策略与一个有界理性的替代方案进行比较，该方案使用一种远为简单的近视放弃阈值，以及与一种仅决定是否开始追求目标的简单启发式方法进行比较。在不同环境中比较策略，我们探讨了规避完整理性计算负担的成本和行为影响。