I offer a variant on the hostage negotiator here. In this variant, the hostage negotiator is replaced by somebody with a purse, and the hostage taker is replaced by a purse snatcher.

As a point of comparison to the purse snatching scenario, consider the following toy-getting scenario:

Whenever a certain parent takes a certain child shopping, the child throws a tantrum unless the child gets a toy. To map this to the purse snatching scenario (and to the other scenarios), the child is A and the parent is B. If the parent convincingly signals a pre-commitment not to get the child a toy, then the child will not bother throwing a tantrum, realizing that it would be futile. If the parent fails to convincingly signal such a pre-commitment, then the child may see an opportunity to get a toy by throwing a tantrum until he gets a toy. The child throwing the tantrum is in effect offering the parent the following trade: get me a toy, and I will stop throwing a tantrum. On future shopping trips, the child implicitly offers the parent the following trade: get me a toy, and I will refrain from throwing a tantrum.

I would call the child an extortionist but I would not call the person with a purse an extortionist, and the main difference I see is that the child is using the threat of trouble to obtain something which was not already their right to have, while the person with the purse is using the threat of trouble to retain something which is their right to keep.