Effects of noise and uncertainty on decision making, evolutionary games and ecological communities

传统的演化系统模型通常是用确定性微分方程来表述的，具有固定的系数，并且相互作用的影响是瞬时的。这种方法忽略了不确定性、固有噪声和延迟的影响。与此同时，噪声在许多进化系统中具有很强的影响，特别是当进化种群很小时。生态群落中的相互作用系数往往是未知的，从而产生不确定性。延迟的影响的反应出现，例如在妊娠期的背景下，或当奖励从行动在游戏中只支付了在稍后的时间。本论文的目的是：（i）开发新的数学方法来研究具有噪声和不确定性的系统，（ii）使用并进一步开发统计物理学的工具来研究进化游戏中延迟和固有噪声的综合影响，（iii）了解在迭代博弈中的噪声采样是否能够识别最优策略。

Traditional models of evolutionary systems are frequently formulated in terms of deterministic differential equations, with fixed coefficients and in which the effects of interactions are instantaneous. This approach neglects the effects of uncertainty, intrinsic noise, and delay. At the same time, noise is known to have strong effects in many evolutionary systems, especially when the evolving population is small. Interaction coefficients in ecological communities are frequently not known, generating uncertainty. Delay in the effects of reactions arise for example in the context of gestational periods, or when rewards from actions in a game are only paid out at a later time.The aims of this thesis are: (i) to develop new mathematical approaches to systems with noise and uncertainty, (ii) to use and further develop tools from statistical physics to study the combined effects of delay and intrinsic noise in evolutionary games, (iii) to understand whether noisy sampling in iterated games can identify optimal strategies.