博彩市场中的在线学习：利润与预测
Online Learning in Betting Markets: Profit versus Prediction
AI总结：
本文研究二元博彩市场中利润与信息获取的根本冲突，提出基于在线学习的定价算法，在几乎不假设投注者信念分布的情况下实现次线性遗憾，并揭示重尾信念分布与利润的关系。
摘要：
我们考察两类二元博彩市场，它们的主要目标分别是获取利润（如体育博彩）或获取信息（如预测市场）。我们阐述了信念与定价之间的相互作用，以分析这两类市场，并证明最大化庄家利润与获取信息这两个目标在根本上是不可兼容的。一个关键见解是，利润取决于（投注者信念分布与真实信念分布之间的）偏差，且投注者信念分布的尾部越重，利润越高。我们的算法贡献在于引入用于定价的在线学习方法。传统上庄家更新价格的频率相当低，我们提出两种算法，在几乎不对投注者信念分布作任何假设的情况下，指导每次看到投注时进行价格更新。该在线定价算法在公平赔率下，针对最差局部最大值实现 $\mathcal{O}(\sqrt{T})$ 的随机遗憾，或以高概率针对全局最大值实现 $\mathcal{O}(\sqrt{T \log T})$ 的遗憾。更广泛地说，二元博彩中利润与信息寻求之间的内在权衡，可能为理解大规模多智能体行为提供新的启发。
英文摘要：
We examine two types of binary betting markets, whose primary goal is for profit (such as sports gambling) or to gain information (such as prediction markets). We articulate the interplay between belief and price-setting to analyse both types of markets, and show that the goals of maximising bookmaker profit and eliciting information are fundamentally incompatible. A key insight is that profit hinges on the deviation between (the distribution of) bettor and true beliefs, and that heavier tails in bettor belief distribution imply higher profit. Our algorithmic contribution is to introduce online learning methods for price-setting. Traditionally bookmakers update their prices rather infrequently, we present two algorithms that guide price updates upon seeing each bet, assuming very little of bettor belief distributions. The online pricing algorithm achieves stochastic regret of $\mathcal{O}(\sqrt{T})$ against the worst local maximum, or $ \mathcal{O}(\sqrt{T \log T}) $ with high probability against the global maximum under fair odds. More broadly, the inherent trade-off between profit and information-seeking in binary betting may inspire new understandings of large-scale multi-agent behaviour.
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。
