Why do children pass in the centipede game? Cognitive limitations v. risk calculations

Abstract

Children and adolescents from 8 to 16 years old play the centipede game in the laboratory, where non-equilibrium behavior (passing) can occur for two reasons: an inability to backward induct (cognitive limitation) or a decision to best respond to the empirical risk and take a measured chance (behavioral sophistication). We find that logical abilities develop gradually. While young participants are (as expected) least likely to perform backward induction, those who do, tend to over-estimate the ability of their peers to behave similarly. With age, participants gradually learn to think strategically and to best respond to their beliefs about others. Overall, the centipede game is an ideal test case for studying the development of abilities, as it disentangles the causes for passing in young children and in teenagers. Interestingly, shrewdness does not transform into earnings, and we document for the first time a game of strategy where payoffs monotonically decrease with age.