Budget Constraints in Prediction Markets
This addresses the problem of how budget constraints affect trader influence in prediction markets, offering insights for market design, but it is incremental as it builds on existing market maker frameworks.
The paper characterizes optimal trades under budget constraints in prediction markets with cost-function-based automated market makers, showing that a generalization of the logarithmic market scoring rule is budget additive, allowing crowds of like-minded traders to combine their impact, while the quadratic rule is not.
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.