Leadership and cooperation in a sequential Prisoner’s Dilemma

In a sequential Prisoner’s Dilemma, conditional cooperation creates an incentive to move second. However, choosing to move first can signal strong social preferences, potentially increasing cooperation when players care not only about actions but also about what those actions reveal about their partners’ social preferences. To examine this, we use the psychological game framework to disentangle the effects of observed actions from those of beliefs about partner preferences. The model yields a separating equilibrium in which players with strong social preferences move first. It predicts that endogenous sorting outperforms exogenous sorting when self-selection is hidden. Full transparency about endogenous sorting may backfire if players forced to move first infer selfish motives and defect. Yet, our experimental data show that transparency is optimal: it boosts incentives to move first and raises cooperation among second movers, without reducing cooperation among those compelled to move first. We also find a notable gender difference, as female subjects are more attuned to the signaling value of moving first.