This paper considers discounted repeated games with boundedly rational players. In each period, player i chooses his current action on the basis of his forecast about the forthcoming n[subscript i] action profiles; his assessment of the payoffs he will obtain next depends on his state of mind, which is non-deterministic. A limited forecast equilibrium is such that after every history the limited horizon forecasts formed by the players are correct. The set of all limited forecast equilibria is characterized and constructed. Application to the repeated prisoner's dilemma shows that limited foresight may sometimes induce purely cooperative paths while purely non-cooperative paths cannot arise. Copyright 2001 by The Review of Economic Studies Limited