Other issue is that it is a hostage situation, and even in normal human hostage situations, whenever you should, or should not give the money to the hostage holder, depends solely to whenever you have higher probability that the hostages will be killed (or tortured) if money are given, than if money are not given.

Actually in real life, we also consider the future consequences of unspecified potential future hostage takers who may be motivated to take hostages if they see a hostage taker paid off. This is ostensibly why the USG will not (directly) pay off a hostage taker.

Also, we have to consider the value of the money, and our next best alternative to saving a hostages life. For example, if Dr. Evil is holding a hostage (doesn't matter who) for $1B, and you know we will not catch him if you pay him off, then you should probably just let him execute the hostage and use the money to buy food for a few thousand starving people somewhere who are just as desperate.