Also known as hallucinatory game. The term hallucinated game was introduced in or shortly before 1914 by the German-American psychologist and philosopher William Lewis Stern (born as Wilhelm Louis Stern, 1871-1938) to denote a child's game in which imaginary objects and scenes are actively created. Although children tend to be quite aware of the unreality of these objects and scenes, they are thought to take on a hallucinatory quality. See also the entry Imaginary companion.
References
Stern, W. (1914). Psychologie der frühen Kindheit bis zum sechsten Lebensjahr. Leipzig: Quelle & Meyer.
Dictionary of Hallucinations. J.D. Blom. 2010.