The intuitive notion of added value in groups represents a fundamental property of biological, physical, and economic systems: how the interaction or cooperation of multiple entities, substances, or other agents can produce synergistic effects. However, despite the ubiquity of group formation, a well-founded measure of added value has remained elusive. Here, we propose such a measure inspired by the Shapley value —a fundamental solution concept from Cooperative Game Theory. To this end, we start by developing a solution concept that measures the average impact of each player in a coalitional game and show how this measure uniquely satisfies a set of intuitive properties. Then, building upon our solution concept, we propose a measure of added value that not only analyzes the interactions of players inside their group, but also outside it, thereby reflecting otherwise-hidden information about how these individuals typically perform in various groups of the population.

中文翻译：

---

群体附加值的衡量标准

直观的概念附加价值在群体中代表了生物、物理和经济系统的基本属性：多个实体、物质或其他代理的相互作用或合作如何产生协同效应。然而，尽管群体形成无处不在，但有充分根据的附加值衡量标准仍然难以捉摸。在这里，我们提出了一项受沙普利值——来自合作博弈论的基本解决方案概念。为此，我们首先开发一个解决方案概念，以衡量平均影响联盟博弈中的每个参与者，并展示该度量如何独特地满足一组直观属性。然后，在我们的解决方案概念的基础上，我们提出了一种附加价值的衡量标准，不仅可以分析玩家之间的互动里面他们的小组，但也外部它，从而反映了有关这些人通常在不同人群中的表现的隐藏信息。