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Cooperative Game Theory of Hierarchies: One Approach to Solving the Low-Risk Puzzle?

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  • Tobias Hiller

    (Department of Microeconomics, University Leipzig, 04107 Leipzig, Germany)

Abstract

In this article, we extend the application of cooperative game theory to the so-called low-risk puzzle. Specifically, we apply concepts that consider hierarchies on the assets in the allocation of portfolio risk. These hierarchies have not previously been considered in portfolio risk allocation using cooperative game theory. We demonstrate our idea through a simulation study. Our results show that considering hierarchies can contribute to solving the low-risk puzzle. Our findings may advance further developments in portfolio theory.

Suggested Citation

  • Tobias Hiller, 2025. "Cooperative Game Theory of Hierarchies: One Approach to Solving the Low-Risk Puzzle?," Risks, MDPI, vol. 13(5), pages 1-20, April.
    • Handle: RePEc:gam:jrisks:v:13:y:2025:i:5:p:86-:d:1646830
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
    3. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    4. Bekaert, Geert & Harvey, Campbell R, 1995. "Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    5. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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