Isabelle Brocas and Juan Carrillo have a new paper in the JPE testing when children develop strategic (k-level) reasoning. A clever game outlined below illustrates the basic idea. Players 1,2 and 3 are asked to make (simultaneous) choices to earn prizes (money for the adults and older kids, points for toys for the younger kids). The sophisticated, rational choice becomes successively more difficult as we from from player 3 to player 1. Player 3 is simply asked to match a shape. In the case shown, for example, player 3 earns the most by choosing the red square labelled C since it matches the shape of the blue square labelled A. Player 2 earns the most by choosing the color chosen by Player 3. Of course, Player 2 doesn’t know what color Player 3 will choose and so has to reason about Player 3’s actions. What color do you choose? Player 1 earns the most by choosing the same letter as Player 2 but now must reason about Player 2 which involves reasoning about how Player 2 will reason about Player 3. What letter do you choose?What do the authors find? First, for both adults and kids either they get it or they don’t. The ones who don’t make the right choice as Player 3 but then randomly choose when playing either Player 2 or Player 1. The ones who get it, play correctly at all three levels. In other words, almost everyone who reasons correct as Player 2 (1-level reasoning) also reasons correctly as Player 1 (2-level reasoning).
Second, there is a marked increase in the ability to perform k-level thinking between ages 8 and 12 but after age 12 (fifth grade) there is shockingly little growth. Together the first and second points suggest that k-level thinking is more of a quantum leap than an evolution in reasoning ability.
Third, most adults reason correctly in this simple game but a significant fraction do not. As the authors put it “some very young players display an innate ability to play always at equilibrium while some young adults are unable to perform two steps of dominance.”
Demographic factors are mostly as expected, children interested in STEM fields perform better (n.b. this implies that contrary to some opinions the STEM set are better at social interaction), kids from better socio-economic backgrounds perform better and slightly unexpected females perform better than males, perhaps because they are more disciplined.
As the authors conclude:
Adolescents are particularly exposed to situations in which strategic sophistication is crucial to avoid wrong decisions. Examples include engaging in risky activities, such as accepting drugs from peers or engaging in unprotected sex. Also, with the development of the internet, naive users are often preyed upon, asked to provide personal information, or tricked into making harmful decisions. Information deliberately intended to deceive young minds also circulates through social media. Making correct decisions in such environments requires understanding the intentions of others and anticipating the consequences of following their advice or opinions. More generally, children and adolescents are gradually discovering the dangers hiding behind social interactions and need to come equipped to detect them, assess them, and navigate around them. We conjecture that failures in these abilities are closely related to underdeveloped logical abilities, and we predict that the level of sophistication of an individual detected through a simple task matches their behavior in social settings.