AI 中文总结
研究预测市场自动做市商损失分布问题，引入均匀自动做市商，用损失与再平衡框架分析，在静态和动态设置下得出相关结论，为做市商设计者和流动性提供者提供控制补贴价格发现成本的方法。
AI 中文摘要
预测市场的自动做市商源自市场评分规则，机制运营商补贴市场以汇总对不确定事件的信念。现有文献关注补贴者的最坏情况总损失，但未涉及损失如何在价格状态或时间上分布。我们使用损失与再平衡框架研究这种分布并引入均匀自动做市商，其瞬时损失与再平衡与资金池价值成比例且与当前代币价格无关。在静态设置中，对于一类广泛的赢鞅，存在实现均匀损失与再平衡的定价函数，反之亦然。我们还将框架扩展到动态流动性管理，表明可随时间调整流动性水平以实现规定的目标预期累积损失计划。通过赢鞅和定价函数的典型例子说明了该理论。我们的结果可为自动做市商设计者和流动性提供者提供信息，说明如何在价格和时间上塑造和控制补贴价格发现的必然成本。
英文摘要
Automated market makers (AMMs) for prediction markets descend from market scoring rules, where a mechanism operator subsidizes a market to aggregate beliefs about uncertain events. The existing literature has focused on bounding the total worst-case loss to the subsidizer, but has not addressed how that loss is distributed across price states or over time. We use the framework of loss-versus-rebalancing (LVR) to study this distribution and introduce \textit{uniform AMMs}, defined by the property that instantaneous LVR is proportional to pool value and independent of the current token price. In a static setting, we show that for a broad class of \textit{win-martingales} -- processes that converge to 0 or 1 at a fixed resolution time -- there exists a pricing function that achieves uniform LVR under that process, and conversely, that any sufficiently regular pricing function induces a win-martingale under which it is uniform. We then extend the framework to dynamic liquidity management, showing that liquidity levels can be adjusted over time to implement a prescribed target expected cumulative loss schedule. This theory is illustrated with canonical examples of win-martingales and pricing functions. Our results can inform AMM designers and liquidity providers on how the inevitable cost of subsidizing price discovery can be shaped and controlled across both price and time.
