Robust permanence and impermanence for stochastic replicator dynamics
Robust permanence and impermanence for stochastic replicator dynamics
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DOI：
10.1080/17513750801915269
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发表时间：
2008-01-01
影响因子：
2.8
通讯作者：
Sandholm, Andwilliam H.
中科院分区：
文献类型：
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作者：
Benaim, Michel;Hofbauer, Josef;Sandholm, Andwilliam H.
Garay 和 Hofbauer (SIAM J. Math. Anal. 34 (2003)) 提出了确定性复制动态的鲁棒持久性和无常性的充分条件。我们在随机复制动力学的背景下重新考虑这些条件，随机复制动力学是通过引入收益的布朗扰动从其确定性模拟中获得的。当确定性复制动力学是永久的并且噪声水平小时，随机动力学允许独特的遍历分布，其质量集中在未扰动系统的最大内部吸引子附近；因此，持久性对于小的无界随机扰动是稳健的。当确定性动力学是无常且噪声水平小或大时，随机动力学以指数速率收敛到状态空间的边界。
Garay and Hofbauer (SIAM J. Math. Anal. 34 (2003)) proposed sufficient conditions for robust permanence and impermanence of the deterministic replicator dynamics. We reconsider these conditions in the context of the stochastic replicator dynamics, which is obtained from its deterministic analogue by introducing Brownian perturbations of payoffs. When the deterministic replicator dynamics is permanent and the noise level small, the stochastic dynamics admits a unique ergodic distribution whose mass is concentrated near the maximal interior attractor of the unperturbed system; thus, permanence is robust against small unbounded stochastic perturbations. When the deterministic dynamics is impermanent and the noise level small or large, the stochastic dynamics converges to the boundary of the state space at an exponential rate.