Final answer:
The responses of children to whether they peeked at cards depend on individual choices and a variety of factors, making it difficult to predict a single outcome. These choices are influenced by game theory dynamics such as the Prisoner's Dilemma and can be shaped by developmental understanding of fairness and self-interest.
Step-by-step explanation:
When children are asked whether they peeked at the cards in the described scenario, their responses can vary widely and cannot be defined by a fixed pattern such as always admitting, always denying, confessing only if caught, or always being truthful.
The scenario parallels the Prisoner's Dilemma from game theory, where individuals must decide between cooperation and self-interest. The dominant strategy, often to confess or admit, arises when an individual perceives that self-interest maximizes their personal benefit regardless of the other's choices. This dynamic is also influenced by experimenter bias and the age-related understanding of concepts like luck and fairness.