In strategic environments where each player's actions reshape what other players can observe, computing equilibria requires tracking an infinite hierarchy of beliefs: what I believe about what you believe about what I believe. This belief hierarchy has resisted exact analysis for forty years. Approximation methods truncate the hierarchy, but the truncation point is arbitrary and the error is uncontrolled.
The first exact equilibrium characterization for finite-player continuous-time LQG games with endogenous signals collapses the hierarchy entirely (arXiv:2603.12140). The key move is conditioning on primitive Brownian shocks rather than the physical state. This is a dynamic analog of Harsanyi's common-prior construction: instead of tracking beliefs about the state, track beliefs about the underlying randomness that generates the state. The infinite hierarchy collapses onto deterministic two-time kernels.
Nash equilibrium reduces to a deterministic fixed point — no truncation, no large-population limit, no approximation. From this characterization emerges an explicit object: the information wedge V^i_t, a deterministic Volterra process that prices the marginal value of shifting opponents' posteriors. The wedge quantifies exactly how much each player benefits from manipulating what others believe.
The wedge vanishes precisely when signals are exogenous — when players' actions don't affect what others observe. This formally delineates the boundary where strategic belief manipulation matters. Below the boundary, standard game theory suffices. Above it, the wedge is the price of information control.