# Budget Constraints in Prediction Markets

arXiv: https://arxiv.org/abs/1510.02045 · HTML: https://mlsanity.com/paper/1510.02045/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2015.

## Built on by (most cited first, 1 of 1)

- [Smooth Quadratic Prediction Markets](https://mlsanity.com/paper/2505.02959/) (2025)

## Abstract (arXiv)

We give a detailed characterization of optimal trades under budget constraints in a prediction market with a cost-function-based automated market maker. We study how the budget constraints of individual traders affect their ability to impact the market price. As a concrete application of our characterization, we give sufficient conditions for a property we call budget additivity: two traders with budgets B and B' and the same beliefs would have a combined impact equal to a single trader with budget B+B'. That way, even if a single trader cannot move the market much, a crowd of like-minded traders can have the same desired effect. When the set of payoff vectors associated with outcomes, with coordinates corresponding to securities, is affinely independent, we obtain that a generalization of the heavily-used logarithmic market scoring rule is budget additive, but the quadratic market scoring rule is not. Our results may be used both descriptively, to understand if a particular market maker is affected by budget constraints or not, and prescriptively, as a recipe to construct markets.