Leadership in a social dilemma: Does it matter if the leader is pro-social or just says they are pro-social?

Previous studies have shown that pro-social leaders cooperate, on average, more than pro-self leaders in social dilemmas. It can, thus, be beneficial for the group to have a pro-social leader. In this paper we analyze the consequences of a leader informing followers that they are pro-social (or pro-self). In doing so, we compare a setting in which the leader's type is truthfully revealed to settings where the leader can 'hide' or 'lie' about their pro-sociality. We find that a leader saying they are pro-social boosts efficiency, even if the signal is not fully credible. Cooperation is highest in a truth setting with a pro-social leader. We demonstrate that these results are consistent with a belief-based model of social preference in which the stated type of the leader changes the frame of reference for followers.