# N-player and Mean-field Games in Ito-diffusion Markets with Competitive or Homophilous Interaction

arXiv: https://arxiv.org/abs/2106.00581 · HTML: https://mlsanity.com/paper/2106.00581/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2021.

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

- [Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approach](https://mlsanity.com/paper/2108.02731/) (2021)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)

## Abstract (arXiv)

In Ito-diffusion environments, we introduce and analyze N-player and common-noise mean-field games in the context of optimal portfolio choice in a common market. The players invest in a finite horizon and also interact, driven either by competition or homophily. We study an incomplete market model in which the players have constant individual risk tolerance coefficients (CARA utilities). We also consider the general case of random individual risk tolerances and analyze the related games in a complete market setting. This randomness makes the problem substantially more complex as it leads to (N or a continuum of) auxiliary ''individual'' Ito-diffusion markets. For all cases, we derive explicit or closed-form solutions for the equilibrium stochastic processes, the optimal state processes, and the values of the games.