Adaptive coordination promotes collective cooperation in repeated social dilemmas

Direct reciprocity based on the repeated prisoner's dilemma has been intensively studied. Most theoretical investigations have concentrated on memory-1 strategies, a class of elementary strategies just reacting to the previous-round outcomes. Though the properties of "All-or-None" strategies (AoN_K) have been discovered, simulations just confirmed the good performance of AoN_K of very short memory lengths. It remains unclear how AoN_K strategies would fare when players have access to longer rounds of history information. We construct a theoretical model to investigate the performance of the class of AoN_K strategies of varying memory length K. We rigorously derive the payoffs and show that AoN_K strategies of intermediate memory length K are most prevalent, while strategies of larger memory lengths are less competent. Larger memory lengths make it hard for AoN_K strategies to coordinate, and thus inhibiting their mutual reciprocity. We then propose the adaptive coordination strategy combining tolerance and AoN_K' coordination rule. This strategy behaves like AoN_K strategy when coordination is not sufficient, and tolerates opponents' occasional deviations by still cooperating when coordination is sufficient. We found that the adaptive coordination strategy wins over other classic memory-1 strategies in various typical competition environments, and stabilizes the population at high levels of cooperation, suggesting the effectiveness of high level adaptability in resolving social dilemmas. Our work may offer a theoretical framework for exploring complex strategies using history information, which are different from traditional memory-n strategies.