The strenght of a little perfection

The paper deals with three related issues. 1. It introduces a measure of partial subgame perfection for equilibria of repeated games. 2. It illustrates that the folk-theorem discontinuity generated by small complexity costs, as exhibited by Abreu and Rubinstein, does not exist in the presence of any level of perfection. 3. It shows that reactive strategy equilibria, such as tit-for-tat, cannot be subgame perfect, even partially so. As a corollary, this shows a need to use full automata rather than exact automata when studying complexity and perfection in repeated games.