Mean Field Portfolio Games with Epstein-Zin Preferences

2025-05-12

AI Summary

This paper investigates a mean-field portfolio game under Epstein–Zin preferences in a non-Markovian framework. Addressing the limitations of conventional power utility, it is the first to incorporate Epstein–Zin preferences into such games and establishes a one-to-one correspondence between Nash equilibria and solutions to a class of nonlinear backward stochastic differential equations (BSDEs). To this end, we develop a stochastic maximum principle tailored to the nonlinearity of Epstein–Zin preferences and introduce a key nonlinear transformation to handle utility nesting. Theoretically, we prove existence and uniqueness of the equilibrium solution. Under deterministic market conditions, we derive explicit closed-form expressions for both investment and consumption strategies—substantially generalizing classical mean-field equilibrium results obtained under power utility. This work provides novel analytical tools and foundational insights for macro-finance modeling with non-exponential time preferences.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary stochastic maximum principle tailored to Epstein-Zin utility and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for the equilibrium investment and consumption policies.

Problem

• Study mean field portfolio games with Epstein-Zin preferences
• Establish uniqueness via Nash equilibria and BSDE solutions
• Derive explicit equilibrium policies in deterministic settings

Innovation

• Epstein-Zin preferences in mean field games
• BSDEs for Nash equilibrium correspondence
• Closed-form equilibrium policies derivation