Using Feasible Action-Space Reduction by Groups to fill Causal Responsibility Gaps in Spatial Interactions

Ashwin George; Vassil Guenov; Arkady Zgonnikov; David A. Abbink; Luciano Cavalcante Siebert

cs.MAFeb 25, 2026

Using Feasible Action-Space Reduction by Groups to fill Causal Responsibility Gaps in Spatial Interactions

Authors: Ashwin George, Vassil Guenov, Arkady Zgonnikov, David A. Abbink, Luciano Cavalcante Siebert

Organizations: Delft University of Technology, The Netherlands · Centre for Meaningful Human Control

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Feasible action space reduction [ 17 ] : For the robot crossing (a) represented in the grid world (b), the feasible action space reduction (FeAR) imposed by actors on affected agents are computed based on the feasible actions of the affected when actors follow their Move de Riguer (MdR) (represented by ) and how many of these are rendered infeasible by the actual actions of actors (represented by ). For affected agent 2, (c) shows how agent 1 reduces the feasible action space by two, (d) shows how 5 on its own has no influence, and (e) shows how the group $\left\{5,7\right\}$ reduces the feasible action space by two.

Panel of Figure 2 — Figure 2: Types of assertive influence based on group FeAR: For the illustrative scenario (a) where three agents are moving towards each other, we show how counterfactuals based on the MdR of actors (b) are used to compute iFeAR values (c) for individual actors and gFeAR values for group actors (d). While iFeAR can only identify solo influences ( $1\nolinebreak\leftharpoonup\nolinebreak 2$ and $2\nolinebreak\leftharpoonup\nolinebreak 1$ ) (e), analysing gFeAR can reveal additional mediated ( $2\nolinebreak\leftharpoonup_{1}\nolinebreak 3$ ) (f) and coupled ( $3\nolinebreak\Leftarrow\nolinebreak\left\{1,2\right\}$ ) (g) influences. Even though $\mathrm{FeAR}_{3,3}<1$ reflects the reduction in feasible action space of 3, iFeAR cannot identify the assertive actors; which are revealed by gFeAR ( $3\nolinebreak\Leftarrow\nolinebreak\left\{1,2\right\}$ ). Also note that agent 3 has no influence on agent 1 as $\mathrm{FeAR}_{2,1}=\mathrm{FeAR}_{\left\{2,3\right\},1}$ .

\begin{array}[]{l r}\phi_{j}\leftarrow\{i:\mathrm{FeAR}_{i,j}<0\}&\text{Find courteous agents

\phi_{j}

.}\\ \kappa_{j}\leftarrow\neg j\setminus\phi_{j}&\text{Remove

\phi_{j}

from candidate agents

\kappa_{j}

.}\\ \mathcal{R}_{0}\leftarrow\emptyset&\text{

\mathcal{R}{n} $--- Assertive agents until$ \mathbb{T}{j,n}

.}\\ \textbf{for }n=1,2,\dots:&\text{For each tier,}\\ \hskip 8.19447pt\mathbb{T}_{j,n}\leftarrow\emptyset&\\ \hskip 8.19447pt\textbf{for }k=1,\dots,|\kappa_{j}|:&\text{starting with k=1,}\\ \hskip 8.19447pt\hskip 8.19447pt\textbf{for all }G\subseteq\kappa_{j},|G|=k:&\text{loop through groups with k agents,}\\ \hskip 8.19447pt\hskip 8.19447pt\hskip 8.19447pt\textbf{if }\mathrm{FeAR}_{\mathcal{R}_{n-1}\cup G,j}>\mathrm{FeAR}_{\mathcal{R}_{n-1},j}:&\text{identify assertive groups,}\\ \hskip 8.19447pt\hskip 8.19447pt\hskip 8.19447pt\hskip 8.19447pt\mathbb{T}_{j,n}\leftarrow\mathbb{T}_{j,n}\cup\{G\},&\text{add them to tiers, and}\\ \hskip 8.19447pt\hskip 8.19447pt\hskip 8.19447pt\hskip 8.19447pt\kappa_{j}\leftarrow\kappa_{j}\setminus G&\text{remove them from candidate agents.}\\ \hskip 8.19447pt\textbf{if }\mathbb{T}_{j,n}=\emptyset:\textbf{ break}&\\ \hskip 8.19447pt\mathcal{R}_{n}\leftarrow\mathcal{R}_{n-1}\cup\bigcup_{G\in\mathbb{T}_{j,n}}G&\end{array}

Algorithm 1 Tiering the assertive influence of agents

Panel of Figure 4 — Figure 4: Ranking the assertiveness of agents into tiers $\mathbb{T}_{j,n}$ : In this illustrative scenario (a), when considering agent 1 as the affected, iFeAR only show agent 6 as being the assertive (b). However, counterfactuals with groups (c) reveal more assertive influences on agent 1 which are systematically ranked into tiers $\mathbb{T}_{1,n}$ (d).

Panel of Figure 6 — Figure 6: S1: Uncovering group effects with group FeAR: For the robot crossing scenario from Fig. 1 , represented in the grid world as in (a), compared to just using iFeAR (b), we are able to uncover more assertive influences using gFeAR, either through the Shapley values (c) or tiers (d). For example, while iFeAR only shows the assertive influence of the robot 5 on pedestrians 3, 4 and 6, both Shapley values and tiers show that 5 is assertive towards all the pedestrians.

Table 1: Ranks of assertive influence in S1: Ranking of assertive influence calculated using FeAR, tiers from group FeAR and Shapley values of group FeAR. ‘

\blacksquare

’ show affected agents which are not considered in the rankings.

Panel of Figure 8 — Figure 8: Emergence of group effects in randomised simulations: Different simulation scenarios are shown in (a). Difference in the number of assertive agents $\Delta_{j}^{\mathrm{Assertive}}$ identified using individual FeAR (iFeAR) and (tiers of) group FeAR (gFeAR) for different proximity to the affected agent are shown in (b). Rankings made using FeAR, tiers from gFeAR or Shapley values of gFeAR we compared using Kendall’s $\tau$ . Variation of Kendall’s $\tau$ with respect to the scenarios and median Manhattan distance between agents is shown in (c).

Causal Attribution

Causal attribution identifies which features, actions, or mechanisms make a difference to an outcome using causal models and interventions.

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Learning Probabilistic Responsibility Allocations for Multi-Agent Interactions

Isaac Remy, Caleb Chang, Karen Leung

University of Washington, Department of Aeronautics and Astronautics · NVIDIA

Multi-Agent Systems

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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.

Abstract

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