Reconstructing the Dark Forest as a Bayesian Game: Exact Conditions for Concealment, Pre-emption and Credible Contact

The Dark Forest hypothesis treats cosmic silence as the strategic consequence of uncertainty, catastrophic vulnerability and incentives for pre-emptive attack. Its central conclusion is usually stated intuitively rather than derived from an explicit incomplete-information game. This paper develops the Bayesian Dark Forest Game, a signalling game between a detected civilisation of privately known type and a receiver choosing whether to wait or strike. The model derives an exact posterior threshold and likelihood-ratio test for rational pre-emption. It proves that uncertainty alone is insufficient: a Dark Forest regime additionally requires catastrophic stakes, a hostile hazard, an effective offensive option, weak gains from peaceful contact and the absence of a credible signal that hostile types cannot imitate. A sender-side exposure condition separates rational concealment from receiver aggression. Pooling and separating Perfect Bayesian Equilibria show when universal concealment is sustainable and when costly authentication permits cautious contact. Extensions incorporate ambiguity aversion and light-speed delay through an endogenous hostile hazard. Numerical regimes demonstrate that defence dominance, conditional pre-emption and near-universal suspicion arise from distinct parameter combinations. The Dark Forest is therefore a contingent equilibrium region, not a theorem of cosmic sociology.