Young infants cannot appreciate the carnival game in which a pea seems to disappear from under a walnut because they have not yet developed a sense of .

The correct answer is object permanence.

Explanation:

According to Piaget, at the time of the sensorimotor stage, the understanding of the fact that the object prevails and the incidences take place autonomously irrespective of one's own activities is known as object permanence. Object permanence signifies that even if the object is hidden it still prevails. In order to develop object permanence, there is a need to develop a tendency to produce a mental representation of the object, which is also known as a schema.  

Thus, in the given case, the young infants cannot appreciate the disappearance of a pea under a walnut as they have not developed a sense of object permanence.