Smooth Quadratic Prediction Markets

2025-05-05

AI Summary

This paper addresses the limitation of learning algorithms in prediction markets constrained by the dual cost function framework. We propose a novel market mechanism that explicitly embeds generalized steepest descent into the pricing rule—the first such design. The mechanism preserves core axioms: instantaneous pricing, information aggregation, no-arbitrage, and incentive compatibility—while significantly reducing worst-case monetary loss under logarithmic loss. Key contributions include: (1) decoupling price updates from fee structures; (2) achieving strict incentive compatibility under budget constraints and one-sided trading (buy-only) via quadratic smoothing and dual decomposition; and (3) establishing an adaptive liquidity analysis framework. Compared to traditional dual cost function-based market makers (DCFMMs), our approach provides a theoretical foundation for tunable-liquidity market design and extends the class of learnable algorithms supported by prediction markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 AD Prediction Market. Our results suggest future designs where the price update rule is separate from the fee structure, yet guarantees are preserved.

Problem

• Design prediction markets inspired by learning algorithms beyond Follow-The-Regularized-Leader
• Propose Smooth Quadratic Prediction Market for steepest gradient descent incentives
• Analyze trading behavior under bounded budgets and buy-only securities constraints

Innovation

• Decomposing DCFMM for gradient descent markets
• Better worst-case loss with preserved axioms
• Adaptive liquidity via separate price rules