This paper advances a single, falsifiable thesis: classical game theory's treatment of belief as a static probability distribution is structurally insufficient to explain strategic behavior, and the missing mechanism is Strategic Theory of Mind (SToM)—an agent's active, dynamic, and recursive capacity to model the minds of others within a decision environment. To formalize this claim, the paper proposes a four-layer framework in which self-interest (Layer 1) operates within incentive structures (Layer 2), is mediated by SToM (Layer 3), and is transformed over time through the discount factor γ into cooperative equilibria grounded in trust (Layer 4). SToM is further decomposed into three operationally distinct modes: analytic (explicit inference from observable behavior and known incentives), simulation-based (projecting oneself into the other's strategic position), and recursive (higher-order modeling of what others believe one will do). Each layer logically presupposes the one below it; each enables phenomena not reducible to lower-layer mechanisms alone. The framework converses with behavioral game theory, cognitive hierarchy models, common knowledge epistemology, and Theory of Mind research, and is extended to organizational leadership and human–AI interaction. A light formal notation is offered linking SToM depth, γ, and equilibrium type as a foundation for future empirical and computational operationalization.