协同进化网络上的自适应循环支配博弈：数值和解析结果
Adaptive cyclically dominating game on co-evolving networks: Numerical and analytic results
摘要：
提出了一种协同进化和自适应的Rock（R）-Paper（P）-Scissors（S）游戏（ARPS），其中智能体使用三种循环主导策略之一，并进行了数值和解析研究。一个代理采取自适应行动，以实现一个邻居，他的优势，通过重新布线一个不满意的链接概率$p$或切换策略的概率$1-p$。数值结果表明，在稳定状态下的两个阶段。$p<p_{\text{cri}}$的活动阶段具有一个使用不同策略的代理的连接网络，这些代理不断交互并采取自适应动作。$p>p_{\text{cri}}$的冻结阶段有三个单独的代理集群，分别使用R、P和S，并终止自适应操作。本文给出了一种一般意义上的协进化网络中链路密度的平均场论，该理论可以很容易地应用于其它多策略协进化网络问题。分析结果与ARPS仿真结果吻合较好。我们指出，不同的概率赢，输，并提请代理之间的游戏分析和模拟结果之间的小差异的起源。由于自适应行动，更高程度的代理往往是那些被利用。度小于（大于）平均度的代理人获胜的概率大于失败的概率。这些结果对于将来试图建立更精确的理论是有用的。
英文摘要：
A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability $p$ or switching strategy with a probability $1-p$. Numerical results revealed two phases in the steady state. An active phase for $p<p_{\text{cri}}$ has one connected network of agents using different strategies who are continually interacting and taking adaptive actions. A frozen phase for $p>p_{\text{cri}}$ has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory of link densities in co-evolving network is formulated in a general way that can be readily modified to other co-evolving network problems of multiple strategies. The analytic results agree with simulation results on ARPS well. We point out the different probabilities of winning, losing, and drawing a game among the agents as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are useful in future attempts on formulating more accurate theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
