Rotations: Matching schemes that efficiently preserve the best reply structure of a one shot game

Suppose that we have a two player game in which we want to test experimentally whether the subjects learn to play the game theoretic solution. For this purpose we need a matching scheme which assures that a rational subject behaves in each round of the experiment as if he played a separate stage game. In this paper we show that such a 'best-reply-structure-preserving matching scheme' has to be free of repercussion effects, and that the rotation of two equally sized groups of subjects, which was introduced by Cooper, DeJong, Forsythe and Ross, solves the problem efficiently.