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The core is a dominant solution concept in economics and cooperative gametheory; it is predominantly used for profit, equivalently cost or utility,sharing. This paper demonstrates the versatility of this notion by proposing acompletely different use: in a so-called investment management game, which is agame against nature rather than a cooperative game. This game has only oneagent whose strategy set is all possible ways of distributing her money amonginvestment firms. The agent wants to pick a strategy such that in each ofexponentially many future scenarios, sufficient money is available in the rightfirms so she can buy an optimal investment for that scenario. Such a strategyconstitutes a core imputation under a broad interpretation, though traditionalformal framework, of the core. Our game is defined on perfect graphs, since themaximum stable set problem can be solved in polynomial time for such graphs. Wecompletely characterize the core of this game, analogous to Shapley and Shubikcharacterization of the core of the assignment game. A key difference is thefollowing technical novelty: whereas their characterization follows from totalunimodularity, ours follows from total dual integrality

The Investment Management Game: Extending the Scope of the Notion of Core