School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK.
Max Planck Institute for Evolutionary Biology, Plön, 24 306, Germany.
Sci Rep. 2020 Oct 14;10(1):17287. doi: 10.1038/s41598-020-74181-y.
Memory-one strategies are a set of Iterated Prisoner's Dilemma strategies that have been praised for their mathematical tractability and performance against single opponents. This manuscript investigates best response memory-one strategies with a theory of mind for their opponents. The results add to the literature that has shown that extortionate play is not always optimal by showing that optimal play is often not extortionate. They also provide evidence that memory-one strategies suffer from their limited memory in multi agent interactions and can be out performed by optimised strategies with longer memory. We have developed a theory that has allowed to explore the entire space of memory-one strategies. The framework presented is suitable to study memory-one strategies in the Prisoner's Dilemma, but also in evolutionary processes such as the Moran process. Furthermore, results on the stability of defection in populations of memory-one strategies are also obtained.
记忆策略是一套迭代囚徒困境策略，因其数学可解性和对单一对手的表现而受到赞誉。本文研究了具有对手思维理论的最佳响应记忆策略。研究结果表明，通过展示最优策略并不总是专横的，从而补充了专横策略并非总是最优的文献。此外，这些结果还提供了证据表明，在多主体交互中，记忆策略受到其有限记忆的限制，并且可以被具有更长记忆的优化策略超越。我们已经开发了一种理论，该理论允许我们探索记忆策略的整个空间。提出的框架适用于研究囚徒困境中的记忆策略，也适用于进化过程，如 Moran 过程。此外，还获得了记忆策略种群中背叛稳定性的结果。
