Sequence of opponents and reduced strategies

We consider the framework of repeated two-person zero-sum games with lack o f information on one side. We compare the equilibrium payoffs of the inform ed player in two cases: where he is facing either a) a single long-lived un informed player, or b) a sequence of short-lived uninformed players. We sho w: 1) that situation b) is always (weakly) better than a), 2) that it can b e strictly better in some cases, 3) that the two cases are equivalent if th e long uninformed player has an optimal strategy independent of his own mov es.