Repeated Games with Asymptotically Finite Horizons

We study a class of repeated games in which the discount factor falls asymptotically to zero through time (reflecting, for example, a vanishing probability of continuation). For an important class of stage games, we give a condition on the sequence of discount factors that is necessary and sufficient for the existence of non-degenerate equilibria. We also study the properties of the equilibrium set when this condition is satisfied.