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

In the repeated Prisoner's Dilemma, predictions are notoriously difficult. Recently, however, Blonski, Ockenfels, and Spagnolo (2011, BOS) showed that experimental subjects predictably cooperate when the discount factor exceeds a particular threshold. I show that this threshold implies existence of an equilibrium robust to two standard refinement assumptions (utility perturbations and imperfect monitoring). The equilibrium is "Semi-Grim": Cooperate after mutual cooperation, defect after mutual defection, randomize otherwise. Testing six resulting predictions on existing data, comprising 37.000 observations, I then find that subjects indeed play Semi-Grim strategies, and switch to cooperation in round 1, when the former turn into equilibria -- at the BOS-threshold