The Investment Management Game: Extending the Scope of the Notion of Core
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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 investment management game, under which an agent needs to allocate her money among investment firms in such a way 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. We study a restriction of this game to 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 total unimodularity, ours follows from total dual integrality. The latter is another novelty of our work.
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