A Causal Approach to Game Theory

The tension between rational and irrational behaviors in human decision-making has been acknowledged across a wide range of disciplines, from philosophy to psychology, neuroscience to behavioral economics. Models of multi-agent interactions, such as von Neumann and Morgenstern's expected utility theory and Nash’s game theory, provide rigorous mathematical frameworks for how agents should behave when rationality is sought. However, the rationality assumption has been extensively challenged, as human decision-making is often irrational, influenced by biases, emotions, and uncertainty, which may even have a positive effect in certain cases. Behavioral economics, for example, attempts to explain such irrational behaviors, including Kahneman's dual-process theory and Thaler's nudging concept, and accounts for deviations from rationality. In this paper, we analyze this tension through a causal lens and develop a framework that accounts for rational and irrational decision-making, which we term Causal Game Theory. We then introduce a novel notion called counterfactual rationality, which allows agents to make choices leveraging their irrational tendencies. We extend the notion of Nash Equilibrium to counterfactual actions and Pearl Causal Hierarchy (PCH), and show that strategies following counterfactual rationality dominate strategies based on standard game theory. We further develop an algorithm to learn such strategies when not all information about other agents is available.