The approval mechanism solves the prisoner's dilemma theoretically and experimentally

Consider a situation where players in a prisoner's dilemma game can approve or reject the other's choice such as cooperation or defection. If both players approve the other's choice, the outcome is the one they chose, whereas if either one rejects the other's choice, the outcome is the one when both defect, which we name the approval mechanism herein (this is inspired by the Cold War doctrine of mutually assured destruction). Experimentally, we find that the cooperation rate with the approval mechanism is 90% in round one and averages 93.2% across the 19 rounds. The questionnaire analysis also allows us to find that subjects' behavior is consistent with subgame perfect elimination of weakly dominated strategies (SPEWDS) rather than Nash equilibrium (NE) or subgame perfect Nash equilibrium (SPNE) behavior. Theoretically, this mechanism implements cooperation in SPEWDS, but not in NE or SPNE.