Calibrated Agents as Market Makers: Automated Liquidity Provision for Long-Tail Prediction Markets

Under what conditions can a forecasting agent profitably provide liquidity on a prediction market? We derive a decomposition of the optimal market-making spread into a microstructure term and an adverse selection term proportional to the agent's mean absolute estimation error~$\alpha$. The profitability condition $s > 2\varphi\alpha$ depends only on the sign of per-fill profit and holds for any positive fill-rate function. A threshold theorem shows that tolerable calibration error increases with existing market spread---a comparative static suggesting that calibrated agents may add the most value on illiquid long-tail markets that lack human market makers. Monte Carlo simulations across 3{,}000 synthetic markets calibrated to empirical Polymarket parameters ($\kappa = 36$) show win rates near 68--70\% across calibration levels, with mean profit varying by $3.4\times$ (\$5.83 to \$1.72), confirming that calibration quality drives profit magnitude. On the empirical side, the main finding is a calibration gap: five frontier LLMs evaluated on 15 resolved Polymarket questions reveal that market-alignment error (MAD $\leq$ 0.029) underestimates true estimation error ($\alpha$ up to 0.437) by an order of magnitude---a result with implications for any system using market prices as calibration targets. The model omits inventory risk and multi-agent competition, limiting direct deployment conclusions, but the spread decomposition provides a tractable framework for analyzing when AI-agent liquidity provision is viable. JEL Classification: D47 , G14 , G17 , C63