# When Shall I Be Empathetic? The Utility of Empathetic Parameter Estimation in Multi-Agent Interactions

arXiv: https://arxiv.org/abs/2011.02047 · HTML: https://mlsanity.com/paper/2011.02047/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Games](https://mlsanity.com/paper/2207.01773/) (2022)
- [Value Approximation for Two-Player General-Sum Differential Games with State Constraints](https://mlsanity.com/paper/2311.16520/) (2023)
- [Learning Nash Equilibrial Hamiltonian for Two-Player Collision-Avoiding Interactions](https://mlsanity.com/paper/2503.07013/) (2025)
- [PACE: A Framework for Learning and Control in Linear Incomplete-Information Differential Games](https://mlsanity.com/paper/2504.17128/) (2025)
- [Peer-Aware Cost Estimation in Nonlinear General-Sum Dynamic Games for Mutual Learning and Intent Inference](https://mlsanity.com/paper/2504.17129/) (2025)

## Abstract (arXiv)

Human-robot interactions (HRI) can be modeled as dynamic or differential games with incomplete information, where each agent holds private reward parameters. Due to the open challenge in finding perfect Bayesian equilibria of such games, existing studies often consider approximated solutions composed of parameter estimation and motion planning steps, in order to decouple the belief and physical dynamics. In parameter estimation, current approaches often assume that the reward parameters of the robot are known by the humans. We argue that by falsely conditioning on this assumption, the robot performs non-empathetic estimation of the humans' parameters, leading to undesirable values even in the simplest interactions. We test this argument by studying a two-vehicle uncontrolled intersection case with short reaction time. Results show that when both agents are unknowingly aggressive (or non-aggressive), empathy leads to more effective parameter estimation and higher reward values, suggesting that empathy is necessary when the true parameters of agents mismatch with their common belief. The proposed estimation and planning algorithms are therefore more robust than the existing approaches, by fully acknowledging the nature of information asymmetry in HRI. Lastly, we introduce value approximation techniques for real-time execution of the proposed algorithms.