The Law of Symbolic Attrition: A Formal Theory of Asymmetric Symbolic Utility

We present an axiomatic model of adversarial symbolic interaction rooted in information theory and optimal stopping. Within a stylized continuous-time framework, we show that an Initiator who is committed to sustaining a high-complexity symbolic system faces a cumulative utility that diverges to negative infinity as the commitment horizon grows. By contrast, we model the Responder's position as a real option and characterize the value extraction problem as a strictly concave optimal-stopping problem. We derive a closed-form Dominance Coefficient c(L0)c(L_0)c(L0), giving the measure of parameter configurations under which engagement is profitable for the Responder. In high-complexity regimes, this coefficient decays inversely in the base complexity L0L_0L0, so that long-run initiation becomes generically loss-making while profitable response opportunities become measure-zero in the limit.