Not Playing by the Rules: Exploratory Play, Rational Action, and Efficient Search

Abstract

Recent studies suggest children's exploratory play is consistent with formal accounts of rational learning. Here we focus on the tension between this view and a nearly ubiquitous feature of human play: In play, people subvert normal utility functions, incurring seemingly unnecessary costs to achieve arbitrary rewards. We show that four-and-five-year-old children not only infer playful behavior from observed violations of rational action (Experiment 1), but themselves take on unnecessary costs during both retrieval (Experiment 2) and search (Experiments 3A-B) tasks, despite acting efficiently in non-playful, instrumental contexts. We discuss the value of such apparently utility-violating behavior and why it might serve learning in the long run.

Keywords: exploration; play; preschoolers; rational action.

Figure 1.

Stimuli used in Experiment 1. Each story showed two characters either efficiently or inefficiently completing a task. (A) Asked to retrieve sticks to make a fire, one character reaches efficiently for sticks on the ground and the other reaches inefficiently for sticks on a tree. (B) Asked to retrieve a key from the red box, one character runs efficiently in a straight line and the other hops inefficiently in a spiral. (C) When taking the elevator to go home, one character presses just one button and the other presses all the buttons. (D) Children preferentially identified the inefficient actor as the one who was playing. Error bars show 95% bootstrapped confidence interval on the average response.

Figure 2.

Experiment 2. Participants completed one Instrumental trial and one Play trial. Half the participants were assigned to the Instrumental pencils task and Play stickers task; the other half were assigned to the Instrumental stickers task and Play pencils task. Here, one child (A) efficiently retrieved pencils but later (B) took the high cost, inefficient action of walking in a spiral for the stickers. Another child (C) efficiently walked in a straight line to the stickers but then (D) took the high cost, inefficient action of jumping up to get the out of reach pencils. To best illustrate the tasks for each condition, here we presented two children who both got the Instrumental condition first and then the Play condition. However, order was counterbalanced throughout such that half the children got the instrumental condition first and half the Play condition first. (E) Our pre-registered analysis (combining tasks) found that children take low-cost, efficient actions (going straight to the target) in Instrumental conditions and high-cost, inefficient actions (taking unnecessary detours, jumping for out-of reach objects) in Play conditions. Post-hoc analyses found that in both tasks, numerically more children take high-cost actions during Play, but the effect was only significant within the Stickers task. Error bars show bootstrapped 95% confidence intervals.

Figure 3.

Experiment 3 materials. In Experiment 3, a target was equally likely to be found in a smaller or larger search space. On the Boxes task, children searched for a ball in either a shelf with 12 boxes or a shelf with 1 box. On the Buttons task, children searched for a music button on a toy with 8 buttons or a toy with 2 buttons. Children completed one Instrumental trial where the target served a functional goal (to play with a ramp toy in the Boxes task or to make a robot dance in the Buttons task), then one Play trial (“hide and seek”) without any functional goals. Task was counterbalanced between trials.

Figure 4.

Experiment 3: Children’s choice of low or high-cost actions in Instrumental and Play conditions. (A) Our pre-registered analysis, finding that four and five-year-olds take low-cost, efficient actions (searching the smaller search space) in Instrumental conditions but high-cost, inefficient actions (searching the larger search space) in the Play conditions. Three-year-olds showed a similar pattern but the effect was not significant because many three-year-olds chose the larger space even in the Instrumental condition. (B) Post-hoc analyses showing that four and five-year-olds take more high-cost actions during Play than the Instrumental condition in each of the two tasks, although the effect was only significant for the Buttons task in the replication experiment. Three-year-olds a similar, non-significant trend in the Boxes task but no effect in the Buttons task. Error bars show bootstrapped 95% confidence intervals above the mean.

Figure 5.

Age differences in search efficiency in Experiment 3B (n = 69). Older children were increasingly likely to make low-cost, efficient choices in the Instrumental search task (green line). However, in play, children of all ages preferred the larger search space. Each circle represents the choice of one participant and lines show predicted probability of making each choice across the ages tested; shaded regions indicate 95% confidence intervals.