Budget Constraints in Prediction Markets

Nikhil Devanur, Miroslav Dudik, Zhiyi Huang, David Pennock
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:49-58, 2015.

Abstract

An automated market maker is a natural and common mechanism to subsidize information acquisition, revelation, and aggregation in a prediction market. The sought-after prediction aggregate is the equilibrium price. However, traders with budget constraints are restricted in their ability to impact the market price on their own. We give a detailed characterization of optimal trades in the presence of budget constraints in a prediction market with a cost-function-based automated market maker. 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. We show that a generalization of the heavily-used logarithmic market scoring rule is budget additive for affinely independent pay- offs, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-devanur15a, title = {Budget Constraints in Prediction Markets}, author = {Devanur, Nikhil and Dudik, Miroslav and Huang, Zhiyi and Pennock, David}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {49--58}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/devanur15a/devanur15a.pdf}, url = {https://proceedings.mlr.press/r13/devanur15a.html}, abstract = {An automated market maker is a natural and common mechanism to subsidize information acquisition, revelation, and aggregation in a prediction market. The sought-after prediction aggregate is the equilibrium price. However, traders with budget constraints are restricted in their ability to impact the market price on their own. We give a detailed characterization of optimal trades in the presence of budget constraints in a prediction market with a cost-function-based automated market maker. 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. We show that a generalization of the heavily-used logarithmic market scoring rule is budget additive for affinely independent pay- offs, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Budget Constraints in Prediction Markets %A Nikhil Devanur %A Miroslav Dudik %A Zhiyi Huang %A David Pennock %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-devanur15a %I PMLR %P 49--58 %U https://proceedings.mlr.press/r13/devanur15a.html %V R13 %X An automated market maker is a natural and common mechanism to subsidize information acquisition, revelation, and aggregation in a prediction market. The sought-after prediction aggregate is the equilibrium price. However, traders with budget constraints are restricted in their ability to impact the market price on their own. We give a detailed characterization of optimal trades in the presence of budget constraints in a prediction market with a cost-function-based automated market maker. 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. We show that a generalization of the heavily-used logarithmic market scoring rule is budget additive for affinely independent pay- offs, 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. %Z Reissued by PMLR on 04 October 2026.
APA
Devanur, N., Dudik, M., Huang, Z. & Pennock, D.. (2015). Budget Constraints in Prediction Markets. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:49-58 Available from https://proceedings.mlr.press/r13/devanur15a.html. Reissued by PMLR on 04 October 2026.

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