Uniform-Loss Automated Market Making for Prediction Markets
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摘要
This paper develops a framework for designing AMMs in binary prediction markets based on uniform loss-versus-rebalancing (LVR). It defines uniform LVR as instantaneous LVR being proportional to the pool value and independent of the current price, achieved by aligning the AMM’s invariant with a separable win-martingale price process through a boundary-value problem (BVP). The authors prove a bidirectional correspondence: from any separable win-martingale, one can construct a concave pool-value function V solving the uniformity BVP, and conversely, from a regular V one can derive a compatible price process G and clock h so that the AMM is uniform. They extend to dynamic liquidity management, showing that a deterministic liquidity schedule can implement a prescribed target expected cumulative loss, with a closed-form m′(t) under uniform LVR. Canonical examples (Gaussian score dynamics, the most exciting game, CPMM, LMSR) illustrate the construction and the robustness benefits, including minimax fairness and budget legibility. The framework thus links belief dynamics to AMM geometry and enables tailored liquidity deployment to shape price-discovery subsidies across price and time [page::1][page::4][page::12][page::18][page::15][page::23].
