Reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas. Recent experimental findings on networked games suggest that conditional cooperation may also depend on the previous action of the player. We here report on experiments on iterated, multi-player Prisoner's dilemma, on groups of 2 to 5 people. We confirm the dependence on the previous step and that memory effects for earlier periods are not significant. We show that the behavior of subjects in pairwise dilemmas is qualitatively different from the cases with more players; After an initial decay, cooperation increases significantly reaching values above 80%. The strategy of the players is rather universal as far as their willingness to reciprocate cooperation is concerned, whereas there is much diversity in their initial propensity to cooperate. Our results indicate that, for cooperation to emerge and thrive, three is a crowd.