Leadership and cooperation in a sequential prisoners' dilemma
by Eberhard Feess, Steffen Lippert, Jamie Martini-Tibbs, James Tremewan
Abstract: An organizational designer with the objective of achieving mutual cooperation in a sequential Prisoners' Dilemma faces two key questions: Should the order of moves be random or should one of the players be awarded the right to decide who moves first? And if so, should the other player be informed about the endogeneity of moves? To answer these questions, we develop a behavioral game theoretical model and an experiment that allow us to disentangle two important social factors for behavior in such a game: choice reciprocity where a first mover is rewarded by the follower for their cooperation, and selection reciprocity where a player is rewarded for their willingness to take on the risk of moving first. Our model yields a separating equilibrium where only players with high choice reciprocity move first and predicts that endogenous sorting where the other player is unaware of the self-selection outperforms exogenous sorting. By contrast, full transparency may backfire if players who infer they have been compelled to move first by players with low choice reciprocity defect too often. Our data, however, suggest that full transparency is optimal due to selection reciprocity, and because players forced to move first do not cooperate less than in the other treatments.