The paper examines the asymptotic behavior of the set of equilibrium payoffs in a repeated game when there are bounds on the complexity of the strategies players may select. The complexity of a strategy is measured by the size of the minimal automaton that can implement it. The main result is that in a zero-sum game, when the size of the automata of both players go together to infinity, the sequence of values converges to the value of the one-shot game. This is true even if the size of the automata of one player is a polynomial of the size of the automata of the other player. The result for the zero-sum games gives an estimate for the general case. Journal of Economic Literature Classification Numbers: 022, 026.