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.

翻译：基于重复囚徒困境的直接互惠机制已被广泛研究。多数理论分析聚焦于记忆-$1$策略，这类基本策略仅对上一轮结果作出反应。尽管"全有或全无"策略（$AoN_K$）的特性已被揭示，但模拟仅证实了短记忆长度$AoN_K$策略的良好表现。尚不清楚当参与者能获取更长历史轮次信息时，$AoN_K$策略将如何表现。我们构建理论模型研究不同记忆长度$K$下$AoN_K$策略类别的性能，严格推导了收益函数，并证明中间记忆长度$K$的$AoN_K$策略最具优势，而更长记忆长度的策略竞争力较弱。较长的记忆长度使$AoN_K$策略难以实现协调，从而抑制了互惠行为。据此我们提出结合容错机制与$AoN_K$协调规则的自适应协调策略：当协调不足时该策略表现为$AoN_K$行为，当协调充分时则通过持续合作包容对手的偶然偏离。研究发现，该自适应协调策略在多种典型竞争环境中优于经典记忆-$1$策略，并将群体合作水平稳定在高位，表明高阶适应性在解决社会困境中的有效性。本工作可为探索基于历史信息的非传统记忆-$n$策略提供理论框架。