Occasional reflections on Life, the World, and Mathematics

Posts tagged ‘game theory’

The president’s dilemma

In the classic prisoners’ dilemma, two members of a criminal gang have been caught by police. There is enough evidence to convict them of minor crimes, but without testimony from one of them they will receive only a light sentence, say one year in prison. If one of them agrees to cooperate with the investigation, prosecutors will let him out for time served, and be able to send the other to prison for ten years. But if they both cooperate with the investigation, both will go to prison for five years (perhaps because the prosecutors will have their information, but not their testimony). Key to the game is that the players are unable to coordinate their strategy. Clearly the best for both of them would be to keep quiet, but the strategy of cooperating with the investigation is superior, from their private perspective, regardless of what the other player does. So they both talk, and both get heavy sentences.

One weird thing about the story here is that the symmetry really doesn’t make sense. It’s not impossible, but it’s peculiar to imagine prosecutors being so interested in pinning the major crime on someone that they’re willing to let a confederate walk free, but indifferent to who flips on whom. That suggests we consider a less-known hierarchical version of this game, where one player is the powerful boss of a crime syndicate — let’s call him “The President” — and the other one is “The Attorney”, who knows all the details of his crimes, and is sufficiently involved to be criminally liable himself. Let’s call this game “The President’s Dilemma”. (more…)

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