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

The core is a dominant solution concept in economics and cooperative game theory; it is used for profit—equivalently, cost or utility—sharing. Starting with the classic work of Shapley and Shubik [25] on the assignment game, the cores of several natural games have been characterized using total unimodularity. The purpose of our paper is two-fold: Our 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 mathematical framework—of the core. Our game is defined on perfect graphs, since the maximum stable set problem (which plays a key role in this game) can be solved in polynomial time for such graphs. We completely characterize the core of this game, analogous to Shapley and Shubik’s characterization of the core of the assignment game. A key difference is that whereas their characterization follows from total unimodularity, ours follows from total dual integrality.