# Peer-Aware Cost Estimation in Nonlinear General-Sum Dynamic Games for Mutual Learning and Intent Inference

arXiv: https://arxiv.org/abs/2504.17129 · HTML: https://mlsanity.com/paper/2504.17129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Learning Latent Representations to Influence Multi-Agent Interaction](https://mlsanity.com/paper/2011.06619/) (2020)
- [First-Person Activity Forecasting with Online Inverse Reinforcement Learning](https://mlsanity.com/paper/1612.07796/) (2016)
- [Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games](https://mlsanity.com/paper/1909.04694/) (2019)
- [Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions](https://mlsanity.com/paper/2110.01027/) (2021)
- [Game-Theoretic Modeling of Human Adaptation in Human-Robot Collaboration](https://mlsanity.com/paper/1701.07790/) (2017)
- [LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning](https://mlsanity.com/paper/2011.08152/) (2020)
- [Towards Modeling and Influencing the Dynamics of Human Learning](https://mlsanity.com/paper/2301.00901/) (2023)
- [InteRACT: Transformer Models for Human Intent Prediction Conditioned on Robot Actions](https://mlsanity.com/paper/2311.12943/) (2023)
- [Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories](https://mlsanity.com/paper/2301.01398/) (2023)
- [Online Inverse Optimal Control for Control-Constrained Discrete-Time Systems on Finite and Infinite Horizons](https://mlsanity.com/paper/2005.06153/) (2020)
- [When Shall I Be Empathetic? The Utility of Empathetic Parameter Estimation in Multi-Agent Interactions](https://mlsanity.com/paper/2011.02047/) (2020)
- [Multi-Hypothesis Interactions in Game-Theoretic Motion Planning](https://mlsanity.com/paper/2011.06047/) (2020)
- [Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Games](https://mlsanity.com/paper/2207.01773/) (2022)
- [Pontryagin Neural Operator for Solving Parametric General-Sum Differential Games](https://mlsanity.com/paper/2401.01502/) (2024)
- [Intent Demonstration in General-Sum Dynamic Games via Iterative Linear-Quadratic Approximations](https://mlsanity.com/paper/2402.10182/) (2024)

## Abstract (arXiv)

Dynamic game theory is a powerful tool in modeling multi-agent interactions and human-robot systems. In practice, since the objective functions of both agents may not be explicitly known to each other, these interactions can be modeled as incomplete-information general-sum dynamic games. Solving for equilibrium policies for such games presents a major challenge, especially if the games involve nonlinear underlying dynamics. To simplify the problem, existing work often assumes that one agent is an expert with complete information about its peer, which can lead to biased estimates and failures in coordination. To address this challenge, we propose a nonlinear peer-aware cost estimation (N-PACE) algorithm for general-sum dynamic games. In N-PACE, using iterative linear quadratic (ILQ) approximation of dynamic games, each agent explicitly models the learning dynamics of its peer agent while inferring their objective functions and updating its own control policy accordingly in real time, which leads to unbiased and fast learning of the unknown objective function of the peer agent. Additionally, we demonstrate how N-PACE enables intent communication by explicitly modeling the peer's learning dynamics. Finally, we show how N-PACE outperforms baseline methods that disregard the learning behavior of the other agent, both analytically and using our case studies