When large trades are not news: Liquidity tail risk and price discovery

When is a large trade news, and when is it a liquidity shock? We study this question in a sequential competitive limit order book with asymmetric information. In our model, liquidity suppliers observe aggregate order flow but not its decomposition into informed demand and uninformed liquidity demand. We model uninformed order flow with Student-$t$ tails, interpreted as a reduced form for rare liquidity regimes. The tail index of liquidity demand determines how informative large trades are. With thin-tailed noise, large order imbalances are quickly interpreted as private information. With heavy-tailed liquidity demand, the same imbalances remain plausibly liquidity-driven. This liquidity-tail ambiguity flattens and concavifies price impact, slows learning from order flow, and delays the decline of adverse-selection premia. We characterize equilibrium through a fixed-point equation for the marginal-cost schedule. Heavy-tailed liquidity demand changes the mathematics of equilibrium: the Gaussian monotonicity and compactness arguments fail because remote liquidity states remain pricing-relevant at polynomial order. We construct fixed points on a tail-controlled compact class and study learning and large-order asymptotics along selected monotone branches. Repeated order flow reveals the fundamental value under stable information-rate conditions, but heavier liquidity tails slow finite-horizon price discovery. Large-order impact obeys regular-variation asymptotics whose exponents depend on the liquidity-tail index, informed competition, and posterior beliefs. The model identifies liquidity tail risk as a state variable for market impact, spread resilience, and the informativeness of large trades.