Prediction markets are powerful mechanisms for information aggregation, but existing designs are optimized for single-event contracts. In practice, traders frequently express beliefs about joint outcomes - through parlays in sports, conditional forecasts across related events, or scenario bets in financial markets. Current platforms either prohibit such trades or rely on ad hoc mechanisms that ignore correlation structure, resulting in inefficient prices and fragmented liquidity. We introduce ParlayMarket, the first automated market-making design that supports parlay-style joint contracts within a unified liquidity pool while maintaining coherent pricing across base markets and their combinations. Our main result is a convergence characterization of the resulting system. Under repeated trading, the AMM dynamics converge to a unique fixed point corresponding to the best approximation to the true joint distribution within the model class. We show that (i) parameter error remains bounded at stationarity due to a balance between signal and noise in trade-induced updates, and (ii) pricing error and monetary loss scale with this parameter error, implying that aggregate market-maker loss remains controlled and grows at most quadratically in the number of base markets. These results establish explicit limits on the information-retrieval error achievable through the trading interface. Importantly, parlay trades play a structural role in this convergence: by providing direct constraints on joint outcomes, they improve identifiability of dependence structure and reduce steady-state error relative to markets that rely only on marginal trades. Empirically, we show both in controlled simulations and in replay on historical Kalshi parlay data that this design achieves the intended scaling while remaining effective in realistic market settings.

翻译：预测市场是信息聚合的强大机制，但现有设计针对单事件合约进行了优化。在实际中，交易者常通过体育中的串关、相关事件的交叉预测或金融市场的情景下注来表达对联合结果的信念。当前平台要么禁止此类交易，要么依赖忽略相关结构的临时机制，导致定价效率低下和流动性碎片化。我们提出ParlayMarket——首个支持在统一流动性池内开展串联合约交易、同时保持基础市场及其组合间定价一致性的自动化做市设计。我们的主要结果是该系统的收敛性刻画：在重复交易下，自动化做市商（AMM）动力学收敛至模型类内对真实联合分布的最佳逼近对应的唯一不动点。我们证明了：(i) 由于交易驱动的更新中信号与噪声的平衡，参数误差在稳态下有界；(ii) 定价误差与货币损失随该参数误差缩放，这意味着做市商的总损失可控且随基础市场数量至多呈二次增长。这些结果确立了通过交易界面可实现的信息检索误差的显式界限。重要的是，串关交易在此收敛中发挥结构性作用：通过对联合结果提供直接约束，相比仅依赖边缘交易的市场，它们提升了依赖结构的可辨识性并降低了稳态误差。在实证中，我们通过受控模拟和历史Kalshi串关数据回放表明，该设计在达到预期缩放效果的同时，在现实市场环境中保持有效性。