Mauricio Gonzalez-Soto

A Random Graph is a random object which takes its values in a space of graphs. We take advantage of the expressibility of graphs in order to model uncertainty about the existence of causal relations within a given set of variables. We adopt a Bayesian point of view which leads us to propose a belief updating procedure with the objective of capturing a causal structure via interaction with a causal environment. Besides learning a causal structure, our proposal is also able to learn optimal actions, i.e., an optimal policy. We test our method in two experiments, each on a different scenario. Our experiments confirm that the proposed technique is able to learn a causal structure as well as an optimal policy. On the other hand, the second experiment shows that our proposal manages to learn an underlying causal model within several tasks in which different configurations of the causal structure are used.

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 surveys 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.

Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models both in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.