Based at the Moffitt Cancer Center, Florida, Cancer Ecology is a small research group led by David Basanta. We are mathematical modellers who work with biologists and clinicians, trying to understand the ecology of tumors and the evolutionary dynamics of cancer progression and resistance to treatment.

The Ransom game

One of the things of being back to the UK is that, once in a while (but hopefully not too often) I can watch TV.

Tonight one of the channels was offering Ransom, the Hollywood movie with Mel Gibson and Rene Russo in which the son of a millionaire is kidnapped for a ransom (2 million dollars). If you had to think of it in terms of game theory, then the payoff table could be something like this:

R K
P (3,3) (0,4)
NP (4,0) (1,1)

Where rows represent the parents of the kidnapped kid and the columns represent the payoffs of the kidnapper. It basically means that the best outcome for the parents is to have the kid released without having to pay whereas the best outcome for the kidnapper is to be paid and still kill the kid (since the kid, once released, could become valuable help for the police to catch the kidnapper).

This is a sequential game in which the kidnapper decides his strategy after the parents chose theirs. That means that the kidnapper maximises his payoff by killing the kid regardless of what the parents decide to do. Knowing that, the only rational (within the rules of this game) strategy of the parents is not to pay. This is similar to the well-known prisoners dilemma

Clearly these dynamics do not favour the parents (nor it does the kidnapper) so in the movie Mel Gibson takes the following decision: he will not pay the money to the kidnapper but to anyone that would capture, dead or alive, the kidnapper. If the kidnapper releases the kid then he can walk away unharmed. These changes the game significantly because the strategy of the parents is already decided and seemingly cast in stone. Still, the table could look like this:

                                               
RK
P(3,3)(0,4)
NP(4,0)(0,-5)

In this case, the parents paying would mean that they pay to the kidnapper which we already mention that is an option that has been ruled out. If they don’t pay to the kidnapper they pay to a bounty hunter and we can assume that with a bounty of 2 million dollars, someone will eventually catch and maybe kill the kidnapper (which we represent here as -5 in terms of payoff). If we restrict ourselves to the row in which the parents pay a bounty hunter if the kidnapper does not release the kid by his own means then the rational option for the kidnapper is clearly to release the kid.

Not such a great movie but they writers did really use game theory in a clever and interesting way.

Comments

Monday, 21 Jan 2008

Matt Brown: Hey, I saw that. Kept me entertained.

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