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

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  • Vijay V. Vazirani

Abstract

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

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  • Vijay V. Vazirani, 2023. "The Investment Management Game: Extending the Scope of the Notion of Core," Papers 2302.00608, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2302.00608
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    1. Tamás Király & Júlia Pap, 2008. "Total Dual Integrality of Rothblum's Description of the Stable-Marriage Polyhedron," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 283-290, May.
    2. Péter Biró & Walter Kern & Daniël Paulusma, 2012. "Computing solutions for matching games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 75-90, February.
    3. Hiroshi Nagamochi & Dao-Zhi Zeng & Naohiśa Kabutoya & Toshihide Ibaraki, 1997. "Complexity of the Minimum Base Game on Matroids," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 146-164, February.
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    Cited by:

    1. Vijay V. Vazirani, 2023. "LP-Duality Theory and the Cores of Games," Papers 2302.07627, arXiv.org, revised Mar 2023.

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