Wow! Gabriel Rossman comes up big. Nice article on pirates and "voluntary" exchange.
Excerpt: If we model a bilateral monopoly negotiation only two things should matter. The first is, as always in a game of chicken, the willingness to accept failure. The more willing you appear to walk away, the more bargaining power you have. In a more protracted game this can cash out as willingness to delay which we can treat as a defect-defect outcome on the installment plan. In fact in the Planet Money episode on Somali piracy, the hostage's party did balk and break off negotiations for weeks at a time until the pirates were willing to come down on price.
The other thing that should matter is the capacity to pay. If the pirate knows for an absolute fact that the hostage's people simply can't raise more than a million dollars then it would be pointless for them to demand two million dollars. Of course there is an issue of information asymmetry in that the hostage's party has much better information on its assets than do the pirates and so the pirates may be skeptical of the hostage's party pleading poverty (especially if the hostage has foolishly told them how much money they can get). We see this at work in the TAL story's point that kidnapping insurance holds the condition that you can't tell anyone you have kidnapping insurance.