ϵ-Consistent equilibrium in repeated games

We introduce the concept of ϵ-consistent equilibrium where each player plays ϵ-best response after every history reached with positive probability. In particular, an ϵ-consistent equilibrium induces an ϵ-consistent equilibrium in any subgame reached along the play path. The existence of ϵ-consistent equilibrium is examined in various repeated games. The main result is the existence in stochastic games with absorbing states.