Smooth Quadratic Prediction Markets

TL;DR

This paper introduces the Smooth Quadratic Prediction Market, a new market design inspired by gradient descent algorithms, which improves worst-case loss and maintains key axioms, with potential for adaptive liquidity.

Contribution

It proposes a novel prediction market mechanism based on gradient descent, enhancing loss bounds and preserving key market axioms compared to existing models.

Findings

Better worst-case monetary loss for AD securities

Preserves key market axioms like no arbitrage and expressiveness

Supports adaptive liquidity strategies

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