The core is a dominant solution concept in economics and game theory. In this context, the following question arises, ``How versatile is this solution concept?'' We note that within game theory, this notion has been used for profit -- equivalently, cost or utility -- sharing only. In this paper, we show a completely different use for it: in an {\em investment management game}, under which an agent needs to allocate her money among investment firms in such a way that {\em in each of exponentially many future scenarios}, sufficient money is available in the ``right'' firms so she can buy an ``optimal investment'' for that scenario. We study a restriction of this game to {\em perfect graphs} and characterize its core. Our characterization is analogous to Shapley and Shubik's characterization of the core of the assignment game. The difference is the following: whereas their characterization follows from {\em total unimodularity}, ours follows from {\em total dual integrality}. The latter is another novelty of our work.

翻译：核心是经济学和博弈论中占主导地位的解概念。在此背景下，自然产生以下问题：“这一解概念具有多大的通用性？”我们注意到，在博弈论中，这一概念仅用于利润——等价于成本或效用——的分配。本文展示了其一个全新应用：在“投资管理博弈”中，代理人需要将资金配置给多家投资公司，使得在指数级数量的未来情景中，每家情景下“正确”的公司都持有足够资金，以便代理人能购买该情景下的“最优投资”。我们将该博弈限制在“完美图”上研究，并刻画了其核心的特征。我们的刻画与Shapley和Shubik对指派博弈核心的刻画具有类比性：区别在于，他们的刻画基于“全幺模性”，而我们的刻画基于“全对偶整性”。后者也是本文的另一项创新。