Sequential Causal Normal Form Games: Theory, Computation, and Strategic Signaling

TL;DR

This paper extends classical game theory to sequential causal games incorporating AI causal reasoning, but finds that causal distinctions do not improve strategic outcomes under rational play, highlighting limitations of current models.

Contribution

It introduces Sequential Causal Normal Form Games, proves their computational complexity, and empirically shows causal reasoning offers no strategic advantage under rational equilibrium assumptions.

Findings

Causal distinctions do not improve welfare over classical equilibria.

Backward induction with rational responses eliminates causal advantages.

Theoretical conditions where benefits could emerge are not realized in practice.

Abstract

Can classical game-theoretic frameworks be extended to capture the bounded rationality and causal reasoning of AI agents? We investigate this question by extending Causal Normal Form Games (CNFGs) to sequential settings, introducing Sequential Causal Multi-Agent Systems (S-CMAS) that incorporate Pearl's Causal Hierarchy across leader-follower interactions. While theoretically elegant -- we prove PSPACE-completeness, develop equilibrium refinements, and establish connections to signaling theory -- our comprehensive empirical investigation reveals a critical limitation: S-CNE provides zero welfare improvement over classical Stackelberg equilibrium across all tested scenarios. Through 50+ Monte Carlo simulations and hand-crafted synthetic examples, we demonstrate that backward induction with rational best-response eliminates any strategic advantage from causal layer distinctions. We construct a theoretical example illustrating conditions where benefits could emerge ($\epsilon$-rational satisficing followers), though implementation confirms that even relaxed rationality assumptions prove insufficient when good instincts align with optimal play. This negative result provides valuable insight: classical game-theoretic extensions grounded in rational choice are fundamentally incompatible with causal reasoning advantages, motivating new theoretical frameworks beyond standard Nash equilibrium for agentic AI.