A caregiver returns a specific response after an infant acts a specific social cue. We define this as interaction rules. The caregiver and infant continuously search for and co-create interaction rules in social games. We propose a scheme composed of "making response prediction," "confirming response prediction," and "habituation/dishabituation to response prediction," and developed an infant model composed of response-predictability and response-habituation. The infant generates actions, observes the partner's response, and get to predict them. It identifies relationships between its actions and the responses, and generates actions to confirm specific responses from the caregiver. The interaction is reciprocated as a result. After it is habituated to the responses, it inhibits the confirmation and generates other actions. This makes a chance for other rules. In experiments on caregiver-infant interaction based on this model and using a ball, various patterns of interaction emerged, such as passing the ball back and forth, rolling and catching, feint passing, and role-reversal feint passing. An appropriate habituation speed of the infant supports the emergence. Response-predictability increases when an interaction is reciprocated. Then response-habituation increases and the dyad quits the interaction and search for another rule, indicating that the scheme and the model work.