N-player and mean field games among fund managers considering excess logarithmic returns

Guohui Guan (), Jiaqi Hu () and Zongxia Liang ()
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Guohui Guan: Renmin University of China
Jiaqi Hu: Tsinghua University
Zongxia Liang: Tsinghua University

Annals of Operations Research, 2025, vol. 349, issue 3, No 7, 1663-1691

Abstract: Abstract This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic return. Each fund manager possesses a unique risky asset, and all fund managers can also invest in a public risk-free asset and a public risk asset. We construct both an n-player game and a mean field game (MFG) to address the competition problem under these two criteria. We explicitly define and rigorously solve the equilibrium and mean field equilibrium (MFE) for each criteria. In the four models, the excess logarithmic return as the evaluation criterion of the fund leads to the allocation fractions being constant. The introduction of the public risky asset yields different outcomes, with competition primarily affecting the investment in public assets, particularly evident in the MFG. We demonstrate that the MFE of the MFG represents the limit of the n-player game’s equilibrium as the competitive scale n approaches infinity. Finally, the sensitivity analyses of the equilibrium are given.

Keywords: Portfolio management; Multi-fund manager competition; Excess logarithmic return; n-player game; Mean field game; 91A06; 91A16; 49L20; 91B16; 91B05 (search for similar items in EconPapers)
JEL-codes: C61 C72 G11 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06576-x

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