# Smooth Quadratic Prediction Markets

arXiv: https://arxiv.org/abs/2505.02959 · HTML: https://mlsanity.com/paper/2505.02959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 5 May 2025.

## Builds on (most cited first, 10 of 10)

- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [A Regularized Framework for Sparse and Structured Neural Attention](https://mlsanity.com/paper/1705.07704/) (2017)
- [An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations](https://mlsanity.com/paper/1304.2338/) (2013)
- [A continuous-time approach to online optimization](https://mlsanity.com/paper/1401.6956/) (2014)
- [Online Optimization in Games via Control Theory: Connecting Regret, Passivity and Poincar'e Recurrence](https://mlsanity.com/paper/2106.04748/) (2021)
- [An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets](https://mlsanity.com/paper/2302.00196/) (2023)
- [An Axiomatic Study of Scoring Rule Markets](https://mlsanity.com/paper/1709.10065/) (2017)
- [Budget Constraints in Prediction Markets](https://mlsanity.com/paper/1510.02045/) (2015)

## Abstract (arXiv)

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.