The Mechanism of Manipulation: A General Theory of Dynamically-Stabilized Certainty Traps and Strategic Frame Control

The Bateson Game formalizes frame uncertainty and the emergence of ambiguity versuscertainty traps, but previous work lacked a formal mechanism describing how a strategic actorcan actively engineer such states against an adaptive learner. We provide such a mechanism.We model the interaction as a repeated game where a Sender exercises action-contingentpayoff control by setting frames after observing the Receiver’s action. This captures principal–agent settings with discretionary evaluation and extends Bateson’s Double Bind to dynamic,closed-loop manipulation. We prove that this capability allows the Sender to implement aclosed-loop controller that regulates the learner’s temporal-difference residuals to zero at anexploitative indifference set-point. We provide necessary and sufficient conditions for theexistence of such traps (Theorem 5.1) and prove that the optimal stabilizing policy followsa “bang-bang” structure (Theorem 6.3), effectively providing a game-theoretic derivationof a dynamic analogue of the Double Bind. Finally, we establish that this strategy is anevolutionarily stable strategy (ESS) that strictly dominates static strategies.