Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal domain. We then consider three key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library.

翻译：因果推理与博弈论推理是人工智能及其他众多学科中的基础性课题：本文关注二者的交叉领域。尽管它们具有重要性，但至今仍缺乏一个能够同时支持这两种推理形式的正式框架。我们提出一种以（结构性）因果博弈为形式的解决方案，该方案既可视为将珀尔的因果层级扩展到博弈论领域，也可视为将科勒和米尔奇的多智能体影响图扩展到因果领域。随后我们探讨三个关键问题：（i）博弈中的（因果）依赖性——无论是变量之间还是策略之间——如何以统一且有原则的方式进行建模？（ii）如何在因果博弈中计算因果查询，这需要哪些假设条件？（iii）因果博弈与现有形式化方法相比有何异同？针对问题（i），我们引入机械化博弈，该机制编码了智能体决策规则与支配博弈的分布之间的依赖性。作为对问题（ii）的回应，我们提出预测、干预和反事实的定义，并讨论各自所需的假设条件。关于问题（iii），我们描述了因果博弈与其他形式化方法之间的对应关系，并阐释因果博弈如何用于回答其他因果或博弈模型不支持的问题。最后，借助一个广泛使用的开源Python库，我们重点介绍了因果博弈的可能应用场景。