Sketch of Proof
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.
Read more about this topic: Folk Theorem (game Theory)
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