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how to prove the folk theorem by grim trigger theory

how to prove the folk theorem by grim trigger theory

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Answer #1

Proof by grim trigger theory:

All players start by playing the prescribed action and continue to do so until someone deviates. If player i deviates, all other players switch to picking the action which minmaxes player i forever after. The one-stage gain from deviation contributes 0 to the total utility of player i. The utility of a deviating player cannot be higher than his minmax payoff. Hence all players stay on the intended path and this is indeed a Nash equilibrium.

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