# Many-player games of optimal consumption and investment under relative performance criteria

arXiv: https://arxiv.org/abs/1905.11782 · HTML: https://mlsanity.com/paper/1905.11782/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 3 of 3)

- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms](https://mlsanity.com/paper/2307.06450/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)

## Abstract (arXiv)

We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed form solution for the n-player game and the corresponding mean field game. This solution is unique in the class of equilibria with constant investment and continuous time-dependent consumption, both independent of the wealth of the agent. Compared to the classical Merton problem with one agent, the competitive model exhibits a wide range of highly nonlinear and non-monotone dependence on the agents' risk tolerance and competitiveness parameters. Counter-intuitively, competitive agents with high risk tolerance may behave like non-competitive agents with low risk tolerance.