Finite Automata in Undiscounted Repeated Games with Private Monitoring

I study two-player undiscounted repeated games with imperfect private monitoring. When strategies are restricted to those implementable by nite automata, fewer equilibrium outcomes are possible. When only two-state automata are allowed, a simple strategy, "Win-Stay, Lose-Shift," leads to cooperation. WSLS has the nice property that it is able to endogenously recoordinate back to cooperation after an incorrect signal. I show that WSLS is essentially the only equilibrium that leads to cooperation in the innitely repeated Prisoner's Dilemma game. In addition, it is also an equilibrium for a wide range of 2 x 2 games. I also give necessary and sucient conditions on the structure of equilibrium strategies when players can use strategies implementable by fnite automata.