# A Game-Theoretic Account of Responsibility Allocation

arXiv: https://arxiv.org/abs/2105.09129 · HTML: https://mlsanity.com/paper/2105.09129/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2021.

## Built on by (most cited first, 15 of 15)

- [On Blame Attribution for Accountable Multi-Agent Sequential Decision Making](https://mlsanity.com/paper/2107.11927/) (2021)
- [Actual Causality and Responsibility Attribution in Decentralized Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2204.00302/) (2022)
- [Anticipating Responsibility in Multiagent Planning](https://mlsanity.com/paper/2307.16685/) (2023)
- [Towards Computationally Efficient Responsibility Attribution in Decentralized Partially Observable MDPs](https://mlsanity.com/paper/2302.12676/) (2023)
- [Responsibility in Extensive Form Games](https://mlsanity.com/paper/2312.07637/) (2023)
- [Responsibility Gap in Collective Decision Making](https://mlsanity.com/paper/2505.06312/) (2025)
- [Responsibility Gap and Diffusion in Sequential Decision-Making Mechanisms](https://mlsanity.com/paper/2507.02582/) (2025)
- [Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems](https://mlsanity.com/paper/2605.13077/) (2026)
- [Responsibility-aware Strategic Reasoning in Probabilistic Multi-Agent Systems](https://mlsanity.com/paper/2411.00146/) (2024)
- [Measuring Responsibility in Multi-Agent Systems](https://mlsanity.com/paper/2411.00887/) (2024)
- [A Graph-Theoretical Perspective on Law Design for Multiagent Systems](https://mlsanity.com/paper/2511.06361/) (2025)
- [Computational Grounding of Responsibility Attribution and Anticipation in LTLf](https://mlsanity.com/paper/2410.14544/) (2024)
- [Responsibility in a Multi-Value Strategic Setting](https://mlsanity.com/paper/2410.17229/) (2024)
- [Diffusion of Responsibility in Collective Decision Making](https://mlsanity.com/paper/2506.07935/) (2025)
- [Peer Oversight in Collective Decision Making](https://mlsanity.com/paper/2608.28754/) (2026)

## Abstract (arXiv)

When designing or analyzing multi-agent systems, a fundamental problem is responsibility ascription: to specify which agents are responsible for the joint outcome of their behaviors and to which extent. We model strategic multi-agent interaction as an extensive form game of imperfect information and define notions of forward (prospective) and backward (retrospective) responsibility. Forward responsibility identifies the responsibility of a group of agents for an outcome along all possible plays, whereas backward responsibility identifies the responsibility along a given play. We further distinguish between strategic and causal backward responsibility, where the former captures the epistemic knowledge of players along a play, while the latter formalizes which players -- possibly unknowingly -- caused the outcome. A formal connection between forward and backward notions is established in the case of perfect recall. We further ascribe quantitative responsibility through cooperative game theory. We show through a number of examples that our approach encompasses several prior formal accounts of responsibility attribution.