Answer: Heteronomous morality
Explanation: According to the theory of Piaget on moral development, heteronomous morality is defined as the morality that is being induced from external factors. Children tend to adapt some rule from source e.g.-parents and do not change it as they think the rules are made by figure of authority.
The case mentioned in the question about Kyle states that she has already has rule set-upped in her mind for the game and thus she is not letting anyone change the regulations as she think it is not correct thing to do.
Other options are incorrect because autonomous stage helps in reasoning through morals, cooperation stages states about cooperation development in children morally.