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People often quit waiting for delayed rewards when the exact timing of those rewards is uncertain. This behavior often has been attributed to self-control failure. Another possibility is that quitting is the result of a rational decision-making process in the face of uncertainty, based on the decision-maker's expectations about the possible arrival times of the awaited reward. There are forms of temporal expectations (e.g., heavy-tailed) under which the expected time remaining until a reward arrives actually increases as time elapses. In those cases, the rational strategy is to quit waiting when the expected reward is no longer worth the expected time remaining. To arbitrate between the "limited self-control" and "temporal expectations" accounts of persistence, we measured pupil diameter during a persistence task, as a physiological marker of surprise (phasic responses) and effort (pre-decision diameter). Phasic pupil responses were elevated in response to reward receipt. Critically, the extent to which pupils dilated following rewards depended on the delay: people showed larger pupillary surprise responses the more delayed the reward was. This result suggests that people expect the reward less the longer they wait for it-a form of temporal expectations under which limiting persistence is rational. Moreover, predecision pupil diameter before quit events was not associated with how long the participant had been waiting, but rather, depended on how atypical the quit decision was compared with the participant's usual behavior. These data provide physiological evidence for a temporal expectations account of persistence under temporal uncertainty.
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