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的一个主导性解概念。在此背景下，自然产生如下问题：“这一解概念到底有多通用？”我们注意到，在博弈论中，这一概念目前仅被用于利润——等价地，成本或效用——的分配。本文展示了该概念的一种全新应用：在一种**投资管理博弈**中，代理人需要将她的资金分配给多家投资公司，使得**在指数级多的未来情景中**，在“正确的”公司里有足够资金可用，从而她可以为每一种情景购买“最优投资”。我们研究了该博弈在**完美图**上的限制情形，并刻画了其核心。我们的刻画与Shapley和Shubik对指派博弈核心的刻画相类似。区别在于：他们的刻画依赖于**全幺模性**，而我们的则依赖于**全对偶整数性**。后者是我们工作的另一创新点。