The Official Policy of the United States is and has been for decades that we "don't negotiate with terrorists." It's a great policy, so long as its practiced. It can be difficult for the families of hostages, who really don't care as much about the long term effects, as they do about getting their loved one back. For them, it doesn't matter who spends how much to whom, as long as their loved one walks away, as soon, and as unharmed as possible.
The problem is that if hostage takers get their way, it gives them an incentive to take more hostages. Conversely, if the bad guys realize that hostage taking is a losing proposition, they'll decide against the practice.
I propose (and others have in the past) a policy of Pax Americana. (Pax Britanica for our pals in Britain, and other names for other Nations with the stomach for it.) The policy is simply: if you're stupid enough to attack American Citizens, we will hunt you down and deliver justice to you. Sure, we'll activate the professional Hostage Negotiators, whose job it will be to keep you busy long enough for us to send in an HRT. They will negotiate to the very second that the front door, back door, window, or wall of your lair explodes in their ear.
My message would be clear:
Yep, this will annoy some of our friends, but in return, we will guarantee their citizens safety in the United States, and the moment that their citizen finds itself in trouble inside our Nation, we'll rescue him/her, unless they opt out. And if they get the information needed first, and so decide, we'll allow their mission inside our borders.
A ransom will be paid. It will be the calling card of the designated HRT. The ransom will be paid in ten dimes delivered from the barrel of a 12 gauge shotgun, at the time of rescue, to the bad guy leader, at high velocity, or whomever the team designates to receive payment.
Should a foreign terrorist (or mafia group) kill an American hostage, within 6 months, an operation or ten, will be launched to take out 10x the number of that group as Americans killed. Preferably, it will be the terrorists involved, along with any leadership of it, but it will not be restricted to any identifiable member of the group. We will strike on our timeline, at our convenience, against any member of that group we choose. Only those that disavow themselves and turn themselves into US Forces will be spared potential retaliation.
Pax Americana: Any group that harms Americans anywhere in the world will be paid $1, perhaps a dime more or less, in ransom, in dimes, at the time the HRT arrives to a representative of their choosing, from the barrel of a 12 gauge.
Pax Americana will end the discussion of terrorists and pirates to profit from bad behavior. It will prove unprofitable to harm any American, no matter how stupid he gets.
Pax Americana will recognize that in the process of a Hostage Rescue, the bad guys may kill a hostage. Americans will be given oral rules to live by during such an event, at the time of their departure from the United States. They will understand that the only negotiations will be a delaying operation until their rescue can be effected, but their lives are their responsibility in such an event, and that the HRT will do everything to preserve it, but that it is not their fault for risking their lives to save someone else's hide.
Pax Americana will result in terrorists and pirates taking every precaution to not endanger American lives.