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

arXiv: https://arxiv.org/abs/2605.13077 · HTML: https://mlsanity.com/paper/2605.13077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 56 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 13 of 13)

- [Trustworthy AI: From Principles to Practices](https://mlsanity.com/paper/2110.01167/) (2021)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Trustworthy AI](https://mlsanity.com/paper/2011.02272/) (2020)
- [Towards Formal Definitions of Blameworthiness, Intention, and Moral Responsibility](https://mlsanity.com/paper/1810.05903/) (2018)
- [A Game-Theoretic Account of Responsibility Allocation](https://mlsanity.com/paper/2105.09129/) (2021)
- [Blameworthiness in Multi-Agent Settings](https://mlsanity.com/paper/1903.04102/) (2019)
- [Blameworthiness in Strategic Games](https://mlsanity.com/paper/1809.05485/) (2018)
- [Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games](https://mlsanity.com/paper/1811.07145/) (2018)
- [Automatic Verification of Concurrent Stochastic Systems](https://mlsanity.com/paper/2008.04613/) (2020)
- [Anticipating Responsibility in Multiagent Planning](https://mlsanity.com/paper/2307.16685/) (2023)
- [Formal Modelling of Safety Architecture for Responsibility-Aware Autonomous Vehicle via Event-B Refinement](https://mlsanity.com/paper/2401.04875/) (2024)
- [Concurrent Stochastic Lossy Channel Games](https://mlsanity.com/paper/2311.17037/) (2023)
- [Responsibility-aware Strategic Reasoning in Probabilistic Multi-Agent Systems](https://mlsanity.com/paper/2411.00146/) (2024)

## Built on by (most cited first, 2 of 2)

- [AUDITA: certified auditing and causal attribution of adverse outcomes in autonomous multi-agent systems](https://mlsanity.com/paper/2608.22160/) (2026)
- [HANSARD: A Reference Architecture for Forensic Readiness, Runtime Witnessing, and Graded Attribution in Autonomous Multi-Agent AI Systems](https://mlsanity.com/paper/2608.22512/) (2026)

## Abstract (arXiv)

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.