a b s t r a c tHuman institutional practices often involve competition within a cooperative structure of mutually accepted rules. In a competitive game, for instance, we not only expect adherence to the rules of the game but also expect an opponent who tries to win and, thus, follows a rational game-playing strategy. We had 3-and 5-year-olds (N = 48) play for a prize against an opponent (a puppet) who played either rationally (trying to win) or irrationally (helping the children to win) while either following or breaking the rules of the game. Both age groups performed costly protest against an opponent who followed the rules but played irrationally by helping the children to win. When facing a rule-breaking opponent, 3-year-olds protested only the rule breaches of an irrational opponent but not irrational play. Five-year-olds also protested the rule breaches of a rational opponent, but in contrast to the 3-year-olds, they protested irrational behavior even in the context of rule breaches. Moreover, many children, in particular 3-year-olds, refrained from protesting. These findings suggest that 5-year-olds, but not 3-yearolds, fully understand the dual-level normative structure of cooperatively regulated competition.