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Short summary

It has been shown that adults do not play at equilibrium in the well-known centipede game, a behavior often attributed to failure of backward induction. In a recent study, we asked children and adolescents (ages 8 to 16) to play the centipede game in the laboratory and we leveraged knowledge about developing abilities to assess the contribution of backward induction logic. In line with the literature, we find that the ability to perform backward induction increases with age. However, it predicts behavior only in elementary school children. Starting in middle school, students who reason logically know that the unraveling argument should not be applied blindly. They utilize Theory-of-Mind (ToM) abilities to form beliefs about others’ play and (optimally) refrain from stopping immediately. Developing ToM leads to a gradual decrease in stopping stages with age, which is accompanied by a decrease in payoffs with age. The results indicate that ToM is the key contributor of behavior that helps departing from backward induction when beneficial.

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Task

Participants complete 5 rounds of the centipede game, 4 with 10 stages, 1 with 4 stages.
Story: The Blue and Orange players walk down the street. Whenever a blue house is reached, the Blue player decides whether to stop and collect the payoffs in that house or to continue. Whenever an orange house is reached, the Orange player makes the same decision. If players reach the last house, they have to stop and grab the payoffs in that house

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Participants

315 school-age subjects from 2nd to 10th grade at the Lycée International of Los Angeles (LILA), a French-English bilingual private school in Los Angeles.

Adult control: 72 undergraduates at the University of Southern California

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Predictions

Backward induction logic predicts that the first player stops immediately independently of the length.
The short game serves as diagnostic for backward induction ability: predictions should be met in adults. Compliance should improve as cognitive abilities develop
We however expect players to not stop immediately in the long games in all ages
We expect participants to learn but to never converge to immediate stopping

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Quick results

Stopping immediately in the short game (Round 2) improves with age (as cognition develops)

Stopping immediately is rare in the long game (Round 1). Players who know how to apply backward induction do not stop, suggesting ToM abilities are kicking in.

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Quick results

Participants in all ages learn to decrease stopping times (without converging to Nash equilibrium). Behavior is similar by the last round.

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Reference

I. Brocas and J. Carrillo, ”The centipede game at school: does developing backward induction logic drive behavior? ” LABEL working paper.

Read the paper HERE