Game Theory & its Parental Applications
It’s called the prisoner’s dilemma. It’s a simple problem of game theory with a remarkable number of applications, not the least of which is convincing people that mathematics does indeed have real world applications.
Consider two suspects are detained for their alleged involvement in a crime. The circumstantial evidence is sufficient to send them each to jail for two years. An eye witness account however would turn that into 10 years, so the arresting officer offers the following deal:
“Rat out your partner and we’ll let you go free; provided your partner doesn’t rat you out.” If they both rat the other out, their 10 year sentences will be commuted to 4 for ‘cooperating’ with the police.
The years of sentence vary with who’s explaining the problem, but the solution is always the same. The prisoner’s dilemma is a question of cooperation, not with their captors, but with each other. Clearly, cooperation among prisoners produces the smallest combined jail sentence. It’s the ‘right’ choice. Keep your mouth shut, and you’ll both be free in two years. The mob has been using game theory for decades; they just didn’t know why.
The problem for each prisoner however, is actually to determine what the other will do. If they’ve been separated or simply don’t trust the other, they may not know their partner’s resolve. In the absence of that knowledge, the ‘right’ thing to do changes. Tell it all. Tell them how wretched your partner is. You’ll either get 4 years, or none at all.
See any applications?
Consider two suspects are detained for their alleged involvement in a crime. The circumstantial evidence is sufficient to send them each to jail for two years. An eye witness account however would turn that into 10 years, so the arresting officer offers the following deal:
“Rat out your partner and we’ll let you go free; provided your partner doesn’t rat you out.” If they both rat the other out, their 10 year sentences will be commuted to 4 for ‘cooperating’ with the police.
The years of sentence vary with who’s explaining the problem, but the solution is always the same. The prisoner’s dilemma is a question of cooperation, not with their captors, but with each other. Clearly, cooperation among prisoners produces the smallest combined jail sentence. It’s the ‘right’ choice. Keep your mouth shut, and you’ll both be free in two years. The mob has been using game theory for decades; they just didn’t know why.
The problem for each prisoner however, is actually to determine what the other will do. If they’ve been separated or simply don’t trust the other, they may not know their partner’s resolve. In the absence of that knowledge, the ‘right’ thing to do changes. Tell it all. Tell them how wretched your partner is. You’ll either get 4 years, or none at all.
See any applications?
posted by Sylow_P | 1:11 PM
3 Comments:
I spent the last few years building up an immunity to iocane powder.
"But if it doesn't work, I'll have to drive out there." Reinhard Selten in Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games
I can see what was going on with the two players you've been talking about. But damn, they gambled and ratted each other out and they both lost. Everything. I wonder why they keep playing together.
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