Dynamically Generated Hierarchies in Games of Competition and the Role of Stochastic Fluctuations

我们将考虑在N个物种中发生的与个体竞争的循环博弈，其中每个物种都是r小于N的循环选择的其他物种的猎物。捕食在这里代表一种压制或竞争的实现。除了通过捕食者或猎物的相互作用外，我们认为个体的繁殖、死亡、扩散和突变是潜在网格尺度上的基本过程。在我们预期的合作中，我们希望解决以下问题：对于哪种数字r和N的组合，以及哪种比率的选择，我们可以观察到不同尺度上共存的游戏，比如石头剪刀布游戏的分形，或者形成更大的，相互竞争的领域，在一个领域内的玩家继续玩另一种游戏？2. 我们目前在Gillespie模拟中观察到的在不同空间尺度上推导游戏层次的合适框架是什么？3. 不同来源的随机波动的影响是什么，它们的相对强度在系统规模方面是怎样的？4. 在这些系统中观察到什么样的老化过程？由于固有的、动态生成的多时间尺度和相互竞争的相互作用，我们期望观察到满足物理老化标准的效应。我们游戏的应用范围从微生物系统到生态系统和社会系统。

We shall consider cyclic games of competition with individuals occurring in N species, where each species is the prey of and preys on r smaller than N cyclically chosen other species. Predation here stands for one realization of suppression or competition. Aside from the interaction via predation or prey we consider reproduction, death, diffusion and mutation of individuals as basic processes on the scale of the underlying grid. In our intended collaboration we want to address the following questions: 1. For which combination of numbers r and N and for which choice of rates do we observe coexisting games on different scales like a fractal of rock-paper-scissor games, or the formation of larger, mutually competing domains, where the players inside a domain keep on playing another kind of game? 2. What is a suitable framework to derive the hierarchies of games on different spatial scales which we currently observe in our Gillespie simulations? 3. What is the impact of the different origins of stochastic fluctuations, how does their relative strength scale in terms of the system size? 4. What kind of aging processes are observed in these systems? Due to the inherent, dynamically generated multiple time scales and the competing interactions, we expect to observe effects, which satisfy the criteria of physical aging. Possible applications of our games range from microbial to ecological and social systems.