Match length realization and cooperation in indefinitely repeated games

Experimental studies of infinitely repeated games typically consist of several indefinitely repeated games ("matches") played in sequence with different partners each time, whereby match length, i.e. the number of stages of each game is randomly determined. Using a large meta data set on indefinitely repeated prisoner’s dilemma games (Dal Bó & Fréchette, 2018) we demonstrate that the realized length of early matches has a substantial impact on cooperation rates in subsequent matches. We estimate simple learning models displaying the "power law of practice" and show that participants do learn from match length realization. We then study three cases from the literature where realized match length has a strong impact on treatment comparisons, both in terms of the size and the direction of the treatment effect. These results have important implications for our understanding of how people learn in infinitely repeated games as well as for experimental design.