Within-subject data from sequential social dilemma experiments reveal a correlation of first-and second-mover decisions for which two channels may be responsible, that our experiment allows to separate: i) a direct, preference-based channel that influences both first- and second-mover decisions; ii) an indirect channel, where second-mover decisions influence beliefs via a consensus effect, and the first-mover decision is a best response to these beliefs. We find strong evidence for the indirect channel: beliefs about second-mover cooperation are biased toward own second-mover behavior, and most subjects best respond to stated beliefs. But when first movers know the true probability of second-mover cooperation, subjects' own second moves still have predictive power regarding their first moves, suggesting that the direct channel also plays a role.