区间证券的对数时间预测市场
Log-time Prediction Markets for Interval Securities
摘要：
我们设计了一个预测市场来恢复随机变量的完整且完全通用的概率分布。交易者买卖区间证券，如果结果落入区间，则支付1美元，否则支付0美元。我们的市场采用中央自动做市商的形式，允许交易者以任意精度表示区间端点。我们提出了两种设计，在这两种设计中，市场操作需要时间对数的间隔数（交易者区分），提供了第一个计算有效的市场连续变量。我们的第一个设计复制了流行的对数市场评分规则（LMSR），但操作速度比标准的LMSR指数更快，利用其模块化属性，构建一个平衡的二叉树和分解计算沿树节点。第二种设计由两个或多个并行的LMSR做市商组成，这些做市商调解越来越细粒度的结果分区的子市场。这种设计对于所有操作都保持计算效率，包括跨子市场的套利移除。它为市场设计者增加了两个额外的好处：（1）通过分配不同的流动性值，能够以不同的分辨率表达信息的效用;（2）通过适当降低每个子市场的流动性，能够保证真正的恒定有界损失。
英文摘要：
We design a prediction market to recover a complete and fully general probability distribution over a random variable. Traders buy and sell interval securities that pay \$1 if the outcome falls into an interval and \$0 otherwise. Our market takes the form of a central automated market maker and allows traders to express interval endpoints of arbitrary precision. We present two designs in both of which market operations take time logarithmic in the number of intervals (that traders distinguish), providing the first computationally efficient market for a continuous variable. Our first design replicates the popular logarithmic market scoring rule (LMSR), but operates exponentially faster than a standard LMSR by exploiting its modularity properties to construct a balanced binary tree and decompose computations along the tree nodes. The second design consists of two or more parallel LMSR market makers that mediate submarkets of increasingly fine-grained outcome partitions. This design remains computationally efficient for all operations, including arbitrage removal across submarkets. It adds two additional benefits for the market designer: (1) the ability to express utility for information at various resolutions by assigning different liquidity values, and (2) the ability to guarantee a true constant bounded loss by appropriately decreasing the liquidity in each submarket.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
