提出新型预测市场，让交易者自动实现梯度下降优化。
Smooth Quadratic Prediction Markets
- 通过重构定价机制，引导交易者集体执行梯度下降。
- 在AD证券上最差损失更优，且保持价格存在等核心性质。
- 适合研究激励相容与流动性调节的机制设计者。
当代理人在基于对偶的成本函数预测市场中交易时，其行为等价于遵循正则化跟随算法（Follow-The-Regularized-Leader）。本文探讨是否可采用其他学习算法来启发预测市场设计。通过分解并修改对偶成本函数市场做市商（DCFMM）的定价机制，提出一种新型预测市场——平滑二次预测市场（Smooth Quadratic Prediction Market），该市场激励代理人集体实现通用的梯度下降更新。相较于DCFMM，该市场在AD证券上的最坏情况资金损失更小，同时保留了瞬时价格存在、信息吸收、表达能力、无套利及某种激励相容性等公理保证。为验证其应用潜力，我们独立分析了在预算受限和仅能买入证券这两种现实约束下代理人的交易行为。最后，初步探讨了利用该市场实现自适应流动性的方法。结果表明，未来市场设计可将价格更新规则与费用结构分离，同时维持理论保障。
原文摘要 · Abstract (English)
When agents trade in a Duality-based Cost Function prediction market, they collectively implement the learning algorithm Follow-The-Regularized-Leader. We ask whether other learning algorithms could be used to inspire the design of prediction markets. By decomposing and modifying the Duality-based Cost Function Market Maker's (DCFMM) pricing mechanism, we propose a new prediction market, called the Smooth Quadratic Prediction Market, the incentivizes agents to collectively implement general steepest gradient descent. Relative to the DCFMM, the Smooth Quadratic Prediction Market has a better worst-case monetary loss for AD securities while preserving axiom guarantees such as the existence of instantaneous price, information incorporation, expressiveness, no arbitrage, and a form of incentive compatibility. To motivate the application of the Smooth Quadratic Prediction Market, we independently examine agents' trading behavior under two realistic constraints: bounded budgets and buy-only securities. Finally, we provide an introductory analysis of an approach to facilitate adaptive liquidity using the Smooth Quadratic Prediction Market. Our results suggest future designs where the price update rule is separate from the fee structure, yet guarantees are preserved.
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