More on the "anti-folk" theorem

For discounted repeated games with unobservable individual deviations, Kaneko's “anti-folk theorem” states that the set of Nash-equilibrium plays coincides with the set of sequences of one-shot Nash-equilibrium plays. When the payoff criterion is long-run average, however, Kaneko's characterization is of a different sort. Here we show that with some additional topological assumptions a version of the anti-folk theorem is available under the long-run average criterion which is parallel to the characterization under the discounting criterion.