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：核心是经济学与博弈论中占主导地位的解概念。在此背景下，自然产生如下问题："这一解概念具有多大通用性？"我们注意到，在博弈论中，该概念至今仅用于利润（等价于成本或效用）分配。本文展示了其完全不同的应用场景：在投资管理博弈中，参与者需要将资金分配至各投资公司，使得在指数级数量的未来情景中，能在"正确"的公司中持有充足资金，从而为该情景购买"最优投资"。我们研究了该博弈在完美图上的限制形式，并刻画了其核心的特征。该特征刻画与Shapley和Shubik对指派博弈核心的刻画具有类比性，其差异在于：后者的刻画源于全幺模性，而本文的刻画源于全对偶整数性——这亦是本工作的另一创新点。