Cooperation and Non-halting Strategies

This note is a response to an unpublished paper by Evans and Thomas (1998) of which we have recently become aware. Evans and Thomas (1998) take issue with a paper that we published some years back on ‘Cooperation and Effective Computability’ in repeated games (Anderlini and Sabourian 1995). In that paper we showed that it is only the cooperative equilibria of an infinitely repeated two-player common-interest game with no discounting that survive both the restriction that players’ strategies must be computable, and appropriately computable trembles. Evans and Thomas (1998) assert that our results are seemingly not robust to changes in the set of computable strategies at the disposal of each player. In particular, they claim that our equilibrium selection result does not extend to the case in which players are allowed to choose strategies that halt on certain histories but do not halt on others. The purpose of this note is to show that the claim in Evans and Thomas (1998) is misleading. We present a modification of the set-up of our earlier paper in which the cooperative equilibria are selected when strategies that halt on certain histories and do not halt on others are allowed. Although extensive modifications are required, the proof of this extension of our earlier result runs along the same general line of argument as the original proof. JEL Classification: C72, C73, C79.