I’m confused about your suggested payoffs. It looks to me like in your example, A is indifferent between no one does anything, and B gives in to A’s threats. In this situation there is not even an incentive for A to threaten B.
A black mail situation is a situation where A prefers B to give in, over noting happens. But also if B don’t give in, A have to give up some utility to in order to follow through with their treat. For this situation see my other response.
I’m confused about your suggested payoffs. It looks to me like in your example, A is indifferent between no one does anything, and B gives in to A’s threats. In this situation there is not even an incentive for A to threaten B.
A black mail situation is a situation where A prefers B to give in, over noting happens. But also if B don’t give in, A have to give up some utility to in order to follow through with their treat. For this situation see my other response.