We study the effects of strategy-dependent time delays on the equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays lead to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, the stationary states of such dynamics depend continuously on time delays. We show that in games with an interior stationary state (a globally asymptotically stable equilibrium in the standard replicator dynamics), at certain time delays it may disappear or there may appear another interior stationary state. In the Prisoner's Dilemma game, for time delays of cooperation smaller than time delays of defection, there appears an unstable interior equilibrium, and therefore for some initial conditions the population converges to the homogeneous state with just cooperators.

中文翻译：

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具有策略依赖性时延的种群演化

我们研究了策略依赖性时延对不断发展的群体均衡的影响。众所周知，时间延迟可能会导致动力系统发生振荡。在这里，我们报告一种新颖的行为。我们表明，具有策略相关时间延迟的演化游戏的微观模型导致了新型的复制器动力学。它描述了在使用给定策略的情况下一部分人口的时间演变以及人口规模。与以前的所有模型不同，此类动力学的稳态始终取决于时间延迟。我们证明，在具有内部静止状态（标准复制器动力学中的全局渐近稳定平衡）的游戏中，在某些时间延迟下，它可能消失或出现另一个内部静止状态。在《囚徒困境》游戏中，