论累积优势竞争的持续时间和强度
On the duration and intensity of cumulative advantage competitions
摘要：
技能（适应性）和运气（随机性）在无数系统中作为资源积累动力学的驱动力，长期以来一直困扰着科学家。在实际竞争中出现的无可争议的不平等的推动下，迫切需要更好地理解技能和运气在资源积累中的作用。当这种竞争是由外部性驱动的，如累积优势（CA），富人更富的效果，很少有人知道的基本属性，如其持续时间和强度。在这项工作中，我们提供了一个数学上的理解CA如何加剧了运气的作用，在简单的和良好的研究竞争模型的技能损害。例如，我们表明，如果两个代理人竞争的资源，在每个时间单位顺序到达，一个早期的中风的运气可以放置在一个非常长的一段时间，我们称之为“适者生存的斗争”的现象不太熟练的领导。在没有竞争性条件的情况下，尽管技能较低的人可能有任何早期的运气，但技能较高的人很快就占了上风。我们证明了一个简单的技能和运气竞争模型的持续时间表现出幂律尾CA时，存在，无论技能的差异，这是在尖锐的对比指数尾时，CA是缺席。我们的研究结果不仅对复杂社会系统中的竞争具有重要意义，而且对利用这些模型的背景也具有重要意义。
英文摘要：
The role of skill (fitness) and luck (randomness) as driving forces on the dynamics of resource accumulation in a myriad of systems have long puzzled scientists. Fueled by undisputed inequalities that emerge from actual competitions, there is a pressing need for better understanding the effects of skill and luck in resource accumulation. When such competitions are driven by externalities such as cumulative advantage (CA), the rich-get-richer effect, little is known with respect to fundamental properties such as their duration and intensity. In this work we provide a mathematical understanding of how CA exacerbates the role of luck in detriment of skill in simple and well-studied competition models. We show, for instance, that if two agents are competing for resources that arrive sequentially at each time unit, an early stroke of luck can place the less skilled in the lead for an extremely long period of time, a phenomenon we call "struggle of the fittest". In the absence of CA, the more skilled quickly prevails despite any early stroke of luck that the less skilled may have. We prove that duration of a simple skill and luck competition model exhibit power law tails when CA is present, regardless of skill difference, which is in sharp contrast to exponential tails when CA is absent. Our findings have important implications to competitions not only in complex social systems but also in contexts that leverage such models.
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