Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems

2026-05-13

AI Summary

This study addresses the quantification of causal responsibility among agents in probabilistic multi-agent systems with respect to specific outcomes. By modeling the system as a concurrent stochastic multi-player game, the work proposes a responsibility metric grounded in counterfactual reasoning with backward-looking analysis. It introduces the Shapley value—adapted from cooperative game theory—for the first time into multi-agent responsibility attribution, integrating it with Nash equilibrium to balance individual rewards against assigned responsibilities. The resulting framework unifies formal verification and strategy synthesis to construct a responsibility-aware mechanism that satisfies fairness and consistency properties. Under stable strategies, this approach simultaneously optimizes each agent’s expected reward and its allocated share of responsibility.

Abstract

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.

Problem

• counterfactual reasoning
• causal responsibility
• multi-agent systems
• responsibility allocation
• probabilistic systems

Innovation

• counterfactual reasoning
• Shapley value
• causal responsibility
• multi-agent systems
• Nash equilibrium