Repeated implementation and complexity considerations

A game form is commitment-free if single actions of players do not have physical consequences, i.e., affect the continuation game. Such game can be thought to represent inifinite interaction with complete patience. A choice rule can be Nash implemented via a commitment-free mechanism if and only if it coincides with the feasible set of a normal form game. However, when players are complexity averse (in the lexicographic sense), then any Nash implementable choice rule becomes available. I am very grateful to Matt Jackson and a referee for their comments. I also thank Klaus Kultti and Hannu Salonen for useful conversations.