  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.
