Why not offer the kidnappers something other than what they demand, but something they could not refuse.
For example, take the Lockheed Martin kidnapping that has a deadline of tomorrow. The scumbag kidnappers want all westerners to leave. I suggest telling them that we cannot do that, but we will build them a hospital for children if they release their hostage. I know this will not end kidnappings, and it may cause more of them to happen. But I feel it is worthy of discussion.
OK, I'm off to work now.