Oh yeah, the Folk Theorem is totally consistent with the Nash equilibrium of the repeated game here being ‘everyone plays 30 forever’, since the payoff profile ‘-30 for everyone’ is feasible and individually-rational. In fact, this is the unique NE of the stage game and also the unique subgame-perfect NE of any finitely repeated version of the game.
To sustain ‘-30 for everyone forever’, I don’t even need a punishment for off-equilibrium deviations. The strategy for everyone can just be ‘unconditionally play 30 forever’ and there is no profitable unilateral deviation for anyone here.
The relevant Folk Theorem here just says that any feasible and individually-rational payoff profile in the stage game (i.e. setting dials at a given time) is a Nash equilibrium payoff profile in the infinitely repeated game. Here, that’s everything in the interval [-99.3, −30] for a given player. The theorem itself doesn’t really help constrain our expectations about which of the possible Nash equilibria will in fact be played in the game.
Oh yeah, the Folk Theorem is totally consistent with the Nash equilibrium of the repeated game here being ‘everyone plays 30 forever’, since the payoff profile ‘-30 for everyone’ is feasible and individually-rational. In fact, this is the unique NE of the stage game and also the unique subgame-perfect NE of any finitely repeated version of the game.
To sustain ‘-30 for everyone forever’, I don’t even need a punishment for off-equilibrium deviations. The strategy for everyone can just be ‘unconditionally play 30 forever’ and there is no profitable unilateral deviation for anyone here.
The relevant Folk Theorem here just says that any feasible and individually-rational payoff profile in the stage game (i.e. setting dials at a given time) is a Nash equilibrium payoff profile in the infinitely repeated game. Here, that’s everything in the interval [-99.3, −30] for a given player. The theorem itself doesn’t really help constrain our expectations about which of the possible Nash equilibria will in fact be played in the game.