The dilemma: Two prisoners are interrogated in separate rooms. Each is asked to snitch in exchange for a reduced sentence. Because they’re separated, the prisoners can’t coordinate, but each knows the other is offered the same deal and the interrogator will only offer bargains that increase the combined years of their imprisonment. For example, snitch gets -2 years but snitchee gets +3 years, netting the interrogator +1 year for a successful bargain. So, what will they do?
Result: Of course the better outcome overall is for neither to snitch and the worst is for both to snitch, but the Nobel-Prize-winning observation was that any prisoner faced with this dilemma (once) will always net a lesser sentence if they snitch than if they don’t, no matter what the other decides. This principle is called the Nash equilibrium. It caused quite a stir.
Application: The result above sounds bleak because it is, but real-world analogs of this game are rarely one-offs. For example, if the prisoners expect to play this game an indeterminate number of times, the result above no longer applies. The study of such logic problems and the strategies to solve them is called game theory.
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Summary for the curious:
The dilemma: Two prisoners are interrogated in separate rooms. Each is asked to snitch in exchange for a reduced sentence. Because they’re separated, the prisoners can’t coordinate, but each knows the other is offered the same deal and the interrogator will only offer bargains that increase the combined years of their imprisonment. For example, snitch gets -2 years but snitchee gets +3 years, netting the interrogator +1 year for a successful bargain. So, what will they do?
Result: Of course the better outcome overall is for neither to snitch and the worst is for both to snitch, but the Nobel-Prize-winning observation was that any prisoner faced with this dilemma (once) will always net a lesser sentence if they snitch than if they don’t, no matter what the other decides. This principle is called the Nash equilibrium. It caused quite a stir.
Application: The result above sounds bleak because it is, but real-world analogs of this game are rarely one-offs. For example, if the prisoners expect to play this game an indeterminate number of times, the result above no longer applies. The study of such logic problems and the strategies to solve them is called game theory.
Edit: fixed typo, added headings