# Inverse Learning of the Altruism and Cost Level in Mixed-Individual Mean Field Games

arXiv: https://arxiv.org/abs/2609.13469 · HTML: https://mlsanity.com/paper/2609.13469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Identifiability in inverse reinforcement learning](https://mlsanity.com/paper/2106.03498/) (2021)
- [Individual-Level Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2202.06401/) (2022)
- [Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis](https://mlsanity.com/paper/1305.6323/) (2013)
- [Dynamic driving and routing games for autonomous vehicles on networks: A mean field game approach](https://mlsanity.com/paper/2012.08388/) (2020)
- [Mean Field Models to Regulate Carbon Emissions in Electricity Production](https://mlsanity.com/paper/2102.09434/) (2021)
- [Maximum Causal Entropy IRL in Mean-Field Games and GNEP Framework for Forward RL](https://mlsanity.com/paper/2401.06566/) (2024)
- [Kernel Based Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games](https://mlsanity.com/paper/2507.14529/) (2025)
- [The entry and exit game in the electricity markets: a mean-field game approach](https://mlsanity.com/paper/2004.14057/) (2020)
- [Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems](https://mlsanity.com/paper/2502.11506/) (2025)
- [How can the tragedy of the commons be prevented?: Introducing Linear Quadratic Mixed Mean Field Games](https://mlsanity.com/paper/2409.08235/) (2024)
- [Cooperation, Competition, and Common Pool Resources in Mean Field Games](https://mlsanity.com/paper/2504.09043/) (2025)

## Abstract (arXiv)

Understanding how humans respond to incentives, both at the individual and collective levels, is crucial to the design of effective policies. Within the continuous-time stochastic framework for large interacting populations, mean field games (MFGs) model populations of non-cooperative agents, whereas mean field control (MFC) describes the fully cooperative benchmark, interpreted in our setting as fully altruistic behavior. Mixed-individual MFGs interpolate between these two extremes through a parameter governing the degree of altruism. A central challenge for regulators and policymakers, however, is that intrinsic altruism levels and other private structural parameters, such as individual labor costs, are typically unobservable. To address this challenge, we develop an inverse learning framework for mixed-individual MFGs. Our approach enables the recovery of (latent) altruism and labor cost levels from noisy observations, with experiments demonstrating the feasibility and accuracy of our method. These findings underscore the promise of inverse MFG methodologies for uncovering latent preference structures in large populations, with important implications for incentive design, empirical behavioral modeling, and data-driven policy analysis.