Graphical Models for Decision-Making: Integrating Causality and Game Theory

TL;DR

This paper addresses how to combine causality and game theory within probabilistic graphical models to improve decision-making in strategic environments. It synthesizes core concepts from causality, game theory, and their intersection into frameworks such as MAID, causal games, and causal Bayesian games, and provides practical guidance for elicitation, modeling, and implementation. The contribution includes a unified mathematical framework, illustrative examples, and actionable guidance to translate causal-game analysis from theory into practice, enabling more robust reasoning about interventions in strategic contexts. Overall, the work supports broader adoption of causal-game reasoning across policy, security, economics, and related domains by bridging theoretical developments with pragmatic modeling and elicitation workflows.

Abstract

Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into strategic interactions among stakeholders with competing interests. Integrating these frameworks has led to significant theoretical advancements with the potential to improve decision-making processes. However, practical applications of these developments remain underexplored. To support efforts toward implementation, this paper clarifies key concepts in game theory and causality that are essential to their intersection, particularly within the context of probabilistic graphical models. By rigorously examining these concepts and illustrating them with intuitive, consistent examples, we clarify the required inputs for implementing these models, provide practitioners with insights into their application and selection across different scenarios, and reference existing research that supports their implementation. We hope this work encourages broader adoption of these models in real-world scenarios.

Figures (10)

• Figure 1: Scope of this paper: the yellow blocks represent key concepts discussed within each domain: causality, game theory, and causal game theory. The concepts are grouped into categories that highlight their primary associations, indicated with background in different colors. Arrows indicate the possible extension or adaptation that allows for the transition from one concept to another.
• Figure 2: The relations of the normal-form game (a), extensive-form game (b), and Bayesian game (c). These relations correspond to Example \ref{['ex:normal-form']} for (a), Examples \ref{['ex:extensive-form']} and \ref{['ex:efgsubgame']} for (b), and Example \ref{['ex:bayesian-form']} for (c). In the normal-form game, the deterring and attacking agents make independent decisions that determine their utilities. In contrast, the attacker’s decisions are shaped by the deterrer's actions in the extensive-form game. Lastly, in the Bayesian game, the agents' decisions and utilities are influenced by their individual types and their beliefs about the opponent's type.
• Figure 3: Deterring Game in Extensive-Form
• Figure 4: Elicitation requirements for different game theory models: while the yellow blocks correspond to the different games along with their associated properties, the purple blocks indicate the different pieces of information that are required to be elicited. The arrows indicate what information is relevant to each game.
• Figure 5: Flow of causal reasoning from data to graphical components (causal discovery) and subsequently to causal estimands and estimates (causal inference). While the light blue part indicates at what stage assumptions have to be taken into account, the purple part indicates possible supplementary information from domain experts. Double dipping occurs when data in the causal discovery stage is being reused at the causal inference stage.

Theorems & Definitions (23)

• Definition 1
• Definition 2
• Example 1: Deterring Game in Normal-Form
• Definition 3
• Example 2: Deterring Game in Extensive-Form
• Definition 4
• Definition 5
• Example 3: Deterring Subgame in Extensive-Form
• Definition 6
• Definition 7