A kidnapper takes a hostage and demands that the hostage pay ransom. They then play the following game in extensive form. The hostage may pay the ransom or not. Following that, the kidnapper may kill the hostage or release him. If the hostage is released, he may report the kidnapping to the police or not report it. The kidnapper has utility +5 for getting paid, -2 for having the kidnapping reported, and -1 for killing the hostage. These utilities are additive (for instance, getting paid but also reported is worth 5-2 = 3). Utilities for the hostage are -10 for getting killed, -2 for paying, +1 for reporting, and these are also additive.

Draw the game tree for this game, labeling choosers, choices and payoffs. Find the natural outcome of the game. [It should be the second worst outcome for both players.)

Suppose the hostage could make a convincing threat or promise. What should it be? What is the new outcome? Who benefits?

Suppose that after the hostage makes the convincing threat or promise in c), the kidnapper can make a threat or promise. What should it be? What is the new outcome? Who benefits?

If the hostage is not able to make a convincing threat or promise, but the kidnapper can, what should it be and what is the result?

Suggest some real-life ways that any or all of the above threats and promises might be made credible.