混合策略方法会破坏具有聚类系数的有限种群中的合作稳定性
Mixed strategy approach destabilizes cooperation in finite populations with clustering coefficient
AI总结：
本研究针对演化博弈中不同策略合作水平差异原因不明的问题，探究离散、连续、混合策略在不同聚类系数网络种群囚徒困境中的合作表现，发现聚类系数会影响策略间合作水平差异，混合策略变异性最高，现实环境中合作系统稳健性或受影响。
摘要：
演化博弈论涵盖离散、连续和混合策略，对于理解合作动态至关重要。离散策略涉及确定性行动，其固定概率为1；而连续策略采用中间概率来体现合作程度，并强调期望收益。混合策略虽与连续策略相似，但会基于中间概率下某一时刻选择的行动计算即时收益。尽管以往研究已强调这些策略方法在促进合作方面的不同作用，但这些方法间合作水平存在差异的原因仍不甚明确。本研究探讨了在囚徒困境博弈情境下，尤其是在具有不同聚类系数的网络种群中，这些策略方法如何影响合作。我们的研究超越了现有研究，揭示出这些策略方法间的合作水平差异并非仅存在于有限种群中，还取决于这些种群的聚类系数。在聚类系数非零的种群中，我们通过多次模拟观察到每种策略方法的稳定合作程度各不相同，其中混合策略的变异性最大，其次是连续策略和离散策略。然而，在聚类系数为零的种群中，合作演化的这种变异性有所降低，缩小了不同策略间合作水平的差异。这些发现表明，在更贴近现实的环境中，合作系统的稳健性可能会受到损害，因为通过混合策略和连续策略实现的合作演化会带来一定程度的不可预测性。
英文摘要：
Evolutionary game theory, encompassing discrete, continuous, and mixed strategies, is pivotal for understanding cooperation dynamics. Discrete strategies involve deterministic actions with a fixed probability of one, whereas continuous strategies employ intermediate probabilities to convey the extent of cooperation and emphasize expected payoffs. Mixed strategies, though akin to continuous ones, calculate immediate payoffs based on the action chosen at a given moment within intermediate probabilities. Although previous research has highlighted the distinct impacts of these strategic approaches on fostering cooperation, the reasons behind the differing levels of cooperation among these approaches have remained somewhat unclear. This study explores how these strategic approaches influence cooperation in the context of the prisoner's dilemma game, particularly in networked populations with varying clustering coefficients. Our research goes beyond existing studies by revealing that the differences in cooperation levels between these strategic approaches are not confined to finite populations; they also depend on the clustering coefficients of these populations. In populations with nonzero clustering coefficients, we observed varying degrees of stable cooperation for each strategic approach across multiple simulations, with mixed strategies showing the most variability, followed by continuous and discrete strategies. However, this variability in cooperation evolution decreased in populations with a clustering coefficient of zero, narrowing the differences in cooperation levels among the strategies. These findings suggest that in more realistic settings, the robustness of cooperation systems may be compromised, as the evolution of cooperation through mixed and continuous strategies introduces a degree of unpredictability.
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