A belief-variance threshold for value co-destruction in multi-level generative AI adoption

We study the intra-organizational adoption of generative artificial intelligence (GenAI) as a multi-level Bayesian game played by senior management, departmental units and individual employees. Existing treatments characterize value co-creation through three parameter thresholds (complementarity, investment efficiency, displacement management) but treat the role of information asymmetry only informally, asserting that high belief variance pushes the equilibrium toward co-destruction without deriving the mechanism. The present note fills this gap. Working with an aggregative reduction of the departmental stage game, we prove that expected organizational welfare is strictly decreasing and concave in the variance of beliefs about rivals’ adoption, and we exhibit a closedform critical variance beyond which equilibrium welfare drops below the no-coordination benchmark. This makes information transparency a fourth, analytically explicit lever alongside the three known parameter thresholds. A Monte Carlo experiment with 10,000 replications confirms the monotone decay and locates the empirical critical variance in close agreement with the theoretical value.