Engineered Misunderstanding Under Psychological Warfare: A Bayesian Signaling Game of Felt-Understanding Collapse in the German Atomausstieg

Russian state-sponsored disinformation has been described in policy and the operational literature, but it is less often formalized in game-theoretic terms. Here, a two-layered formal model is developed showing how adversarial perturbation of a communication channel can collapse cross-group felt understanding—the third-order intentional state/belief structure, established empirically by Livingstone, in which one group believes its perspectives are recognized and accepted as valid by another. The Analytical Model is a static Bayesian signaling game with binary types and a noisy channel parameterized by perturbation rate π. The Analytical Model shows that when recognition benefits exceed signaling costs, there exists a perturbation threshold π * = 1 − c R /( u R · p ) above which mutual misrecognition becomes the unique Perfect Bayesian Equilibrium outcome. The Computational Model embeds this logic in an agent-based simulation on a homophilic stochastic block model and scale-free networks with continuous recognition capacity. Four substantive findings emerge: the closed-form analytical threshold from the Analytical Model predicts the boundary of collapse in the dynamic networked simulation; high network homophily protects cooperative behavior below π * but provides no rescue above it; bridge seeding—the placement of recognition-capable agents at structurally central cross-group positions—is the most effective of three policy interventions tested, rescuing cooperation even above π *; and uniform adversarial volume is approximately as damaging as strategically targeted adversarial precision across both small dense and large scale-free topologies, qualifying the operational claim that targeted disinformation should strictly outperform volume-based approaches. The model is illustrated with the German Atomausstieg (nuclear phase-out) case, and implications for clinical psychology, public policy, and intergroup recognition under psychological warfare are discussed.