论文标题
随机空间进化游戏中的复制器方程
The replicator equation in stochastic spatial evolutionary games
论文作者
论文摘要
我们研究了多策略的随机进化游戏，并在扩大尺寸$ n \ to \ infty $的空间种群中进行了死亡出生更新。该模型是选民模型扰动。对于典型的人群，我们需要满足$ 1/n \ ll W \ ll 1 $的扰动强度。在空间上适当的条件下，策略的限制密度过程被证明可以遵守复制器方程，并且归一化的波动会融合到高斯过程，并在限制密度中具有Wright-Fisher协方差功能。作为一种应用，我们从生物学文献的阳性猜想中解决，预期密度在许多非规范图上近似复制器方程。
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\ll w\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the biological literature that the expected density processes approximate the replicator equation on many non-regular graphs.
