I doubt if this is about a Game,he sounds frustrated, as his Dad is away are you making up for it and doing sports and plenty of activities, he could be bored and fed up and what he needs is stimulation, get him and get the Nanny working outside with him, how about Bike Riding, Basket Ball, soccer, what games is he into. Is there any other reason for his tantrums you can think of sometimes there is a trigger point, Try not to feed into his behavior as if it gets him your attention that could be a reason for him to do it,