# How can the tragedy of the commons be prevented?: Introducing Linear Quadratic Mixed Mean Field Games

arXiv: https://arxiv.org/abs/2409.08235 · HTML: https://mlsanity.com/paper/2409.08235/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Inverse Learning of the Altruism and Cost Level in Mixed-Individual Mean Field Games](https://mlsanity.com/paper/2609.13469/) (2026)

## Abstract (arXiv)

In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in real life this phenomenon is often avoided thanks to the underlying altruistic behavior of (all or some of the) agents. Motivated by this observation, we introduce and analyze two different mean field models to include altruism in the decision making of agents. In the first model, mixed individual MFGs, there are infinitely many agents who are partially altruistic (i.e., they behave partially cooperatively) and partially non-cooperative. In the second model, mixed population MFGs, one part of the population behaves cooperatively and the remaining agents behave non-cooperatively. Both models are introduced in a general linear quadratic framework for which we characterize the equilibrium via forward backward stochastic differential equations. Furthermore, we give explicit solutions in terms of ordinary differential equations, and prove the existence and uniqueness results.