论文标题
网络进化游戏中的确定性和随机合作过渡
Deterministic and stochastic cooperation transitions in evolutionary games on networks
论文作者
论文摘要
尽管已经对互动玩家网络出现的合作动态进行了详尽的研究，但尚未完全了解网络互惠何时以及如何驱动合作过渡。在这项工作中，我们通过使用主方程和蒙特卡洛模拟的框架来调查进化社会困境在结构化人群上的关键行为。开发的理论描述了吸收，消除准策略和混合策略的存在以及随着系统的参数的变化，状态之间的过渡性质（连续或不连续）的存在。特别是，当决策过程是确定性的，在费米函数的零有效温度的极限时，我们发现复制概率是系统参数的不连续函数和网络度序列的函数。这可能会导致任何系统大小的最终状态突然变化，这与蒙特卡洛模拟结果非常吻合。我们的分析还揭示了大型系统的连续和不连续相变的存在，随着温度的升高，这在平均场近似中进行了解释。有趣的是，对于某些游戏参数，我们发现最佳的“社交温度”最大化/最大程度地降低了合作频率/密度。
Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we investigate the critical behavior of evolutionary social dilemmas on structured populations by using the framework of master equations and Monte Carlo simulations. The developed theory describes the existence of absorbing, quasi-absorbing, and mixed strategy states and the transition nature, continuous or discontinuous, between the states as the parameters of the system change. In particular, when the decision-making process is deterministic, in the limit of zero effective temperature of the Fermi function, we find that the copying probabilities are discontinuous functions of the system's parameters and of the network degrees sequence. This may induce abrupt changes in the final state for any system size, in excellent agreement with the Monte Carlo simulation results. Our analysis also reveals the existence of continuous and discontinuous phase transitions for large systems as the temperature increases, which is explained in the mean-field approximation. Interestingly, for some game parameters, we find optimal "social temperatures" maximizing/minimizing the cooperation frequency/density.
