Counterfactuals, rationality and equilibrium concepts in game theory

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Strategic decision-making requires careful consideration of the consequences of each available action, necessitating hypotheses about other players' beliefs and potential reactions. Without prior experience, individuals often rely on personal reasoning to justify their strategies, leading to counterfactual dilemmas. For instance, if an unexpected action is taken, will others perceive it as irrational or intentional? Historically, game theorists believed that common knowledge of rationality was sufficient to navigate these counterfactuals. However, by the late 1980s, it became evident that the existing game-theoretic framework lacked a model to effectively address this reasoning, jeopardizing the refinement of its predictions and prescriptions. Introducing a theory to analyze counterfactuals is essential for evaluating player deliberations. Philosopher Robert Stalnaker emphasized that without the ability to deliberate on counterfactuals, players cannot effectively choose actions or comply with suggested equilibria. This work examines the contributions of philosophers David Lewis and Jonathan Bennett in evaluating counterfactual reasoning, analyzing their impact on backward induction and sequential equilibrium. We assess the consistency of their results and the implications of players forming beliefs based on these theories. Our interpretation suggests that while Lewis's approach supports backward induction outcomes, Bennett's m