Glynatsi Nikoleta E, Akin Ethan, Nowak Martin A, Hilbe Christian
Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, Plön 24306, Germany.
Department of Mathematics, The City College of New York, New York, NY 10031.
Proc Natl Acad Sci U S A. 2024 Dec 10;121(50):e2420125121. doi: 10.1073/pnas.2420125121. Epub 2024 Dec 6.
Direct reciprocity is a wide-spread mechanism for the evolution of cooperation. In repeated interactions, players can condition their behavior on previous outcomes. A well-known approach is given by reactive strategies, which respond to the coplayer's previous move. Here, we extend reactive strategies to longer memories. A reactive- strategy takes into account the sequence of the last moves of the coplayer. A reactive- counting strategy responds to how often the coplayer cooperated during the last rounds. We derive an algorithm to identify the partner strategies within these strategy sets. Partner strategies are those that ensure mutual cooperation without exploitation. We give explicit conditions for all partner strategies among reactive-2, reactive-3 strategies, and reactive- counting strategies. To further explore the role of memory, we perform evolutionary simulations. We vary several key parameters, such as the cost-to-benefit ratio of cooperation, the error rate, and the strength of selection. Within the strategy sets we consider, we find that longer memory tends to promote cooperation. This positive effect of memory is particularly pronounced when individuals take into account the precise sequence of moves.
直接互惠是合作进化的一种广泛存在的机制。在重复互动中，参与者可以根据先前的结果来调整自己的行为。一种著名的方法是反应性策略，它会对对手的上一步行动做出回应。在此，我们将反应性策略扩展到更长的记忆。一种反应性策略会考虑对手最后行动的序列。一种反应性计数策略会对对手在最后几轮中合作的频率做出回应。我们推导出一种算法，以识别这些策略集中的伙伴策略。伙伴策略是那些能确保相互合作而不被利用的策略。我们给出了反应性2策略、反应性3策略和反应性计数策略中所有伙伴策略的明确条件。为了进一步探究记忆的作用，我们进行了进化模拟。我们改变了几个关键参数，如合作的成本效益比、错误率和选择强度。在我们考虑的策略集中，我们发现更长的记忆往往会促进合作。当个体考虑行动的精确序列时，记忆的这种积极作用尤为明显。
