  The core is a dominant solution concept in economics and cooperative game
theory; it is predominantly used for profit, equivalently cost or utility,
sharing. This paper demonstrates the versatility of this notion by proposing a
completely different use: in a so-called investment management game, which is a
game against nature rather than a cooperative game. This game has only one
agent whose strategy set is all possible ways of distributing her money among
investment firms. The agent wants to pick a strategy such that 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. Such a strategy
constitutes a core imputation under a broad interpretation, though traditional
formal framework, of the core. Our game is defined on perfect graphs, since the
maximum stable set problem can be solved in polynomial time for such graphs. We
completely characterize the core of this game, analogous to Shapley and Shubik
characterization of the core of the assignment game. A key difference is the
following technical novelty: whereas their characterization follows from total
unimodularity, ours follows from total dual integrality
