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. Phasic pupil responses were elevated in response to reward receipt. 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). In those cases, the rational strategy is to quit waiting when the expected reward is no longer worth the expected time remaining. 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. 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. This behavior often has been attributed to self-control failure.

People often quit waiting for delayed rewards when the exact timing of those rewards is uncertain. This study highlights the effectiveness of robots as a distractor during waiting times and outlines a potential new application of robots in educational contexts. Given the positive implications of strong executive function, how it might be increased in children in which it is lacking, limited, or in the process of developing, is of considerable import. However, when children were exposed to robots and given the opportunity to interact with them, waiting times for the majority of children increased with medium to large effect sizes.

The likelihood of waiting increased over sessions when children were simply asked to wait, but waiting times did not increase further during a condition where teachers offered activities as a distraction. Using a single-case experimental design, the present study exposed 24 preschoolers to three experimental conditions where a choice was provided between an immediately available reward and a delayed but larger reward. Although robots have increasingly been utilized in educational situations that involve teaching psychosocial skills to children, including various aspects related to self-control, the utility of robots in increasing the likelihood of self-imposed delay of gratification remains to be explored. One such skill is the ability to deal with frustrations when waiting for a delayed, preferred reward. The development of executive function (EF) in children, particularly with respect to self-regulation skills, has been linked to long-term benefits in terms of social and health outcomes.

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