While there is an extensive literature on the theory of infinitely repeated games, empirical evidence on how "the shadow of the future" affects behavior is scarce and inconclusive. I simulate infinitely repeated prisoner's dilemma games in the lab with a random continuation rule. The experimental design represents an improvement over the existing literature by including sessions with finite repeated games as controls and a large number of players per session (which allows for learning without contagion effects). I find that the shadow of the future matters not only by significantly reducing opportunistic behavior, but also because its impact closely follows theoretical predictions.
Bó, Pedro Dal.
2005."Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games."American Economic Review,
95(5): 1591-1604.DOI: 10.1257/000282805775014434