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shokwave comments on Real World Solutions to Prisoners' Dilemmas - Less Wrong
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No, it's a game of Chicken.
It's not a Prisoner's Dilemma because when the government pays, the terrorists gain no extra value from killing a hostage.
Also, if the government cooperates, that will encourage other terrorists to take more hostages later on, making the CC payoff unsymmetrical.
I'm actually curious as to whether this has been studied in practice. This is the kind of thing I expect people with big egos to do regardless of whether the actual expected value is positive.
It's not Chicken either, because of the reason you just gave.
Edit: Seeing how this post got downvoted with no reply being posted, I have to assume it was someone who doesn't know much about game theory, so let me explain:
If the terrorists gain no extra value from killing a hostage if the government pays, then DC > CC is false for the terrorist side; however both PD and Chicken are symmetrical problems that require DC > CC to be true for all sides. Therefore, this problem is neither PD nor Chicken.
But the hostages are (presumably) infidels or something enemy-like.
Yes, in that case it would actually be PD.