Human behavior in interactive settings is shaped not only by individual objectives but also by shared constraints with others, such as safety. Understanding how people allocate responsibility, i.e., how much one deviates from their desired policy to accommodate others, can inform the design of socially compliant and trustworthy autonomous systems. In this work, we introduce a method for learning a probabilistic responsibility allocation model that captures the multimodal uncertainty inherent in multi-agent interactions. Specifically, our approach leverages the latent space of a conditional variational autoencoder, combined with techniques from multi-agent trajectory forecasting, to learn a distribution over responsibility allocations conditioned on scene and agent context. Although ground-truth responsibility labels are unavailable, the model remains tractable by incorporating a differentiable optimization layer that maps responsibility allocations to induced controls, which are available. We evaluate our method on the INTERACTION driving dataset and demonstrate that it not only achieves strong predictive performance but also provides interpretable insights, through the lens of responsibility, into patterns of multi-agent interaction.
Figures & tables
Fig. 1 : Bottom left: If all agents behave selfishly, executing their desired control, a collision occurs. So who is “responsible” for deviating from their desired control? Our responsibility generative model encodes the scene context into a latent space (top left), decodes it to a distribution over responsibility allocations (top right), which pass through a responsibility-aware safety filter, producing a multimodal distribution of agent behaviors (bottom right).
Fig. 2 : High-level diagram of the responsibility CVAE with continuous latent space. A distribution over responsibility allocation p(γ∣s) conditioned on scene s is computed as the pushforward distribution of the latent distribution p(z∣s) under the initial part of the decoder gϕ . Responsibility allocation values γ are then passed through the responsibility safety filter to produce predicted agent controls u .
Fig. 3 : Learning synthetic p(γ∣s) . (a) The ground truth distribution of γ1 with respect to agents’ relative x− position; purple represents low densities and yellow represents high density. (b) Estimated distribution of γ1 from a responsibility CVAE with Gaussian latent space. (c) Agent 1’s ground truth x -acceleration vs. x -accel. from conditionally sampled γ1 .
Fig. 4 : Responsibility allocations γ in a traffic intersection from the INTERACTION dataset. Left: The blue car arrives in the interaction first, and is leaving (dashed lines denote past trajectories), while the red car has arrived before green. Right: Estimated probability densities of γ for red vs. green and red vs. blue over time; more yellow means higher density.
Method
ADE (m)
Miss Rate (%)
Direct u prediction
0.140±9.10e-3
1.27%±2.85e-4
Following udesired
0.406±2.26e-3
49.3%±7.27e-3
(1) none
0.221±9.44e-3
9.31%±2.83e-3
(2) softmax
0.178±9.91e-3
10.1%±3.47e-3
(3) clip at 0
0.185±9.76e-3
9.80%±2.83e-3
(4) clip at −β
0.216±9.30e-3
8.74%±2.87e-3
TABLE I : Predicted trajectory performance on INTERACTION data over 1 second prediction horizon. Lower is better.
When multiple agents share a cost budget, a common Lagrange multiplier can enforce the aggregate constraint but does not determine how its penalty should be allocated across agents. Uniform penalties ignore heterogeneity in the rewards agents sacrifice, while agent-specific multipliers may still rely on the same aggregate cost signal. We introduce Lagrangian Responsibility Allocation (LiRA), which learns each agent's share of a common multiplier by optimizing social welfare over a finite training horizon. The multiplier enforces the aggregate budget, while responsibility shares redistribute its influence without modifying the original rewards or constraints. For convex games under standard regularity conditions, varying these shares induces a smooth family of normalized generalized Nash equilibria in which active constraints remain at their budgets while welfare varies. To optimize responsibility before convergence, we derive a welfare gradient that accounts for both learning updates and the induced change in data distribution. Across CityLearn, MABIM, Harvest, and MetaDrive, spanning 3 to 400 agents, LiRA improves average social welfare by up to 29% over uniform and agent-specific multiplier baselines. Grid and driving costs remain within budget, inventory violations decrease, and Harvest makes more effective use of available budget.
Xiaoyang Cao, Jingqi Li, Zhe Fu +1
Massachusetts Institute of Technology · The University of Texas at Austin · Stanford University +1
Responsibility allocation -- determining the extent to which agents are accountable for outcomes -- is a fundamental challenge in the design and analysis of multi-agent systems. In this work, we model such systems as concurrent stochastic multi-player games and introduce a notion of retrospective (backward) counterfactual responsibility, which quantifies an agent's accountability for outcomes resulting from a given strategy profile. To allocate responsibility among agents, we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency. Building on this foundation, we propose a formal framework that supports both verification and strategic reasoning in responsibility-aware multi-agent systems. Furthermore, by adopting Nash equilibrium as the solution concept, we demonstrate how to compute stable strategy profiles in which agents trade off responsibility against expected reward.
Heralding the advent of autonomous vehicles and mobile robots that interact with humans, responsibility in spatial interaction is burgeoning as a research topic. Even though metrics of responsibility tailored to spatial interactions have been proposed, they are mostly focused on the responsibility of individual agents. Metrics of causal responsibility focusing on individuals fail in cases of causal overdeterminism - when many actors simultaneously cause an outcome. To fill the gaps in causal responsibility left by individual-focused metrics, we formulate a metric for the causal responsibility of groups. To identify assertive agents that are causally responsible for the trajectory of an affected agent, we further formalise the types of assertive influences and propose a tiering algorithm for systematically identifying assertive agents. Finally, we use scenario-based simulations to illustrate the benefits of considering groups and how the emergence of group effects vary with interaction dynamics and the proximity of agents.
Ashwin George, Vassil Guenov, Arkady Zgonnikov +2
Delft University of Technology, The Netherlands · Centre for Meaningful Human Control