We study competition over populations (audiences, workers, students, etc.) Understanding how institutions, businesses and technologies offer solutions to diverse populations is increasingly important. We hypothesize a closed-form relationship among the amount of competition, population diversity and quality of solutions offered to populations. Typical homogeneous competition (e.g., in Supply-Demand-Price systems) becomes the special case of competition over populations with infinitesimal diversity, while competition over diverse populations leads to Competition-Diversity-Quality tradeoffs. We formulate this as a conservation-law for competitive systems and demonstrate that quality for population members is a periodic function of competition and diversity there. We consider the competition among movies, restaurants, schools, workers and countries (in world-wide trade).

我们研究人口（观众，工人，学生等）的竞争。了解机构，企业和技术如何为不同人群提供解决方案变得越来越重要。我们假设竞争量，人口多样性和提供给人口的解决方案质量之间存在封闭形式的关系。典型的同质竞争（例如，在供求价格系统中）变成了对具有无限小多样性的种群进行竞争的特例，而对不同种群的竞争导致了竞争-多样性-质量的权衡。我们将其表述为竞争系统的保护法，并证明人口成员的质量是那里竞争和多样性的周期性函数。我们考虑电影，饭店，学校之间的竞争，