Learning in Causal Markov Games

Markov Games are the standard formal model for multi-agent reinforcement learning, capturing agents that act in a shared state and optimize rewards over time. However, in real-world settings, agents’ decisions are often influenced by unobserved factors, such as cognitive biases, behavioral tendencies, or intuitive signals, that also affect rewards and future states. Ignoring these unobserved confounders can make standard learning methods converge to suboptimal policies. In such settings, optimal play may require policies that condition on counterfactual signals, requiring reasoning at the counterfactual layer of the Pearl Causal Hierarchy. In this paper, we introduce Causal Markov Games (CMGs), a framework for modeling sequential multi-agent decision making in the presence of unobserved confounding. We show that CMGs strictly generalize Markov Games, with arbitrarily large gaps between classical interventional equilibria and causal counterparts. We then develop two learning algorithms under different observability assumptions. The first, CNash-VI-FO, is a model-based learner with finite-sample guarantees when agents’ natural actions or intuitions are revealed post hoc. The second, CNash-VI-NO, is an explore-then-exploit procedure with asymptotic guarantees for the setting in which opponents’ natural actions are never observed. To address scalability, we further provide a drop-in counterfactual augmentation of deep MARL. Empirically, on a confounded windy variant of the Multi-Particle Environment and the Iterated Causal Prisoner’s Dilemma, counterfactual agents strictly dominate their non-causal counterparts.