论文标题
更多可以更好：分析单点固定概率函数$ 2 \ times2 $ game
More can be better: An analysis of single-mutant fixation probability functions under $2\times2$ games
论文作者
论文摘要
进化游戏理论已被证明是一种有力的工具，可以通过考虑进化过程中的频率依赖性适应性来探测集体行为的自组织。这表明策略的稳定性不仅取决于每次相遇后收到的收益，还取决于人口的规模。在这里，我们通过分析单个突变体的固定概率作为人口规模的功能，研究$ 2 \ TIME 2 $游戏的有限人群。我们证明，在24场可能的游戏中，有9场总是会导致单调降低功能，类似于固定的健身方案。但是，固定功能显示在12个不同的反协调，协调和优势游戏下的区域增加。也许在违反直觉上，这确定了单点策略通常会受益于在较大的人群中。从全球最小值增加到正渐近值的固定功能无处不在，但可能很容易被弱选择限制所隐藏。我们获得了足够的条件，可以观察到少量人群的固定量增加，这可能会发生三种不同的方式。最后，我们描述了固定功能，在中间人口大小下，在两个极端界定的区域增加的固定功能。我们将它们的发生与从拥有一个全球极端到其他形状的过渡相关联。
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not only on the payoffs received after each encounter but also on the population's size. Here, we study $2\times2$ games in well-mixed finite populations by analysing the fixation probabilities of single mutants as functions of population size. We proved that 9 out of the 24 possible games always lead to monotonically decreasing functions, similarly to fixed fitness scenarios. However, fixation functions showed increasing regions under 12 distinct anti-coordination, coordination, and dominance games. Perhaps counter-intuitively, this establishes that single-mutant strategies often benefit from being in larger populations. Fixation functions that increase from a global minimum to a positive asymptotic value are pervasive but may have been easily concealed by the weak selection limit. We obtained sufficient conditions to observe fixation increasing for small populations and three distinct ways this can occur. Finally, we describe fixation functions with increasing regions bounded by two extremes under intermediate population sizes. We associate their occurrence with transitions from having one global extreme to other shapes.
