Cooperation and Punishment

We show that, in repeated common interest games without discounting, strong `perturbation implies efficiency' results require that the perturbations must include strategies which are `draconian' in the sense that they are prepared to punish to the maximum extent possible. Moreover, there is a draconian strategy whose presence in the perturbations guarantees that any equilibrium is efficient. We also argue that the results of Anderlini and Sabourian (1995) using perturbation strategies which are cooperative (and hence non-draconian) are not due to computability per se but to the further restrictions they impose on allowable beliefs.