# Reasoning about Causality in Games

**Authors:** Lewis Hammond, James Fox, Tom Everitt, Ryan Carey, Alessandro Abate, Michael Wooldridge  
**arXiv:** [2301.02324](https://arxiv.org/abs/2301.02324)  
**Date:** 2023-01-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2301.02324v1/

## Key points

- The paper "Reasoning about Causality in Games" focuses on the intersection of causal reasoning and game-theoretic reasoning.
- The authors propose a formal framework that supports both forms of reasoning through structural causal games.
- The paper considers three key questions: how can the (causal) dependencies in games be modeled in a uniform, principled manner; how may causal queries be computed in causal games, and what assumptions does this require; and how do causal games compare to existing formalisms?
- To address question one, the authors introduce mechanized games that encode dependencies between agents' decision rules and the distributions governing the game.
- For question two, they present definitions of predictions, interventions, and counterfactuals, discussing the assumptions required for each.
- Regarding question three, they describe correspondences between causal games and other formalisms while explaining how causal games can answer queries that other models do not support.
- The paper also highlights possible applications of causal games aided by an extensive open-source Python library.
- One such application is settable systems inspired by generalised structural causal models used to capture optimization, equilibria, and learning.

## Summary

The paper "Reasoning about Causality in Games" addresses the intersection of causal reasoning and game-theoretic reasoning, which are fundamental topics in artificial intelligence and other disciplines. The authors propose a formal framework that supports both forms of reasoning through structural causal games. These games extend Pearl's causal hierarchy to the game-theoretic domain and Koller and Milch's multi-agent influence diagrams to the causal domain. The paper considers three key questions: how can the (causal) dependencies in games be modeled in a uniform, principled manner; how may causal queries be computed in causal games, and what assumptions does this require; and how do causal games compare to existing formalisms? To address question one, the authors introduce mechanized games that encode dependencies between agents' decision rules and the distributions governing the game. For question two, they present definitions of predictions, interventions, and counterfactuals, discussing the assumptions required for each. Regarding question three, they describe correspondences between causal games and other formalisms while explaining how causal games can answer queries that other models do not support. The paper also highlights possible applications of causal games aided by an extensive open-source Python library. One such application is settable systems inspired by generalised structural causal models used to capture optimization, equilibria, and learning. To deal with cycles in these models, intervenable variables are duplicated into response and setting variables indicating which side of the structural function each occurs on. Overall, "Reasoning about Causality in Games" provides a comprehensive framework for understanding causality within game theory while offering practical applications for researchers interested in this area of study.