Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma

A recent advance in our understanding of repeated PDs is the detection of a threshold d* at which laboratory subjects start to cooperate predictively. This threshold is substantially above the classic threshold "existence of Grim equilibrium" and has been characterized axiomatically by Blonski, Ockenfels, and Spagnolo (2011, BOS). In this paper, I derive its behavioral foundations. First, I show that the threshold is equivalent to existence of a "Semi-Grim" equilibrium s_cc>s_cd=s_dc>s_dd. It is cooperative (s_cc>0.5), non-reciprocal (s_cd=s_dc), and robust to imperfect monitoring ("belief-free"). Next, I show that the no-reciprocity condition s_cd=s_dc also follows from robustness to random-utility perturbations (logit equilibrium). Finally, I re-analyze strategies in four recent experiments and find that the majority of subjects indeed plays Semi-Grim when it is an equilibrium strategy, which explains d*'s predictive success.