Iterated prisoner's dilemma

Brad DeLong: I Demand That Cosma Shalizi Write a Weblog Post About What the Real Dyson-Press Contribution to the Theory of Iterated Prisoner's Dilemma Is!

Deviation from behaviour implies a normal centre, this is usually V-Bi and Y-Ro where for example people might be punished for trying to leave a mafia or gang. When these threats are insufficient there can be chaotic edges around y, for example Oy cronies that deviate from serving the normal mafia center. In Ro the chaos occurs from within, like a demonstration mob that attacks R malcontents inside it making it harder to keep a united front against Y.

It depends then on whether the punishments are made when the team is attacking as Y or defending as Ro, there are different outcomes. With Ro an R deviation can become a target to split the team like with Y lions or attacking the weak part of a castle or army. With y an Oy deviation can sometimes cause a rout with a counter attack, also Y loses control of normal policy.

A commonly referenced proof of a folk theorem was published in (Rubinstein 1979).

The method for proving folk theorems is actually quite simple. A grim trigger strategy is a strategy which punishes an opponent for any deviation from some certain behavior. So, all of the players of the game first must have a certain feasible outcome in mind. Then the players need only adhere to an almost GRIM trigger strategy under which any deviation from the strategy which will bring about the intended outcome is punished to a degree such that any gains made by the deviator on account of the deviation are exactly cancelled out. Thus, there is no advantage to any player for deviating from the course which will bring out the intended, and arbitrary, outcome, and the game will proceed in exactly the manner to bring about that outcome.