Belief Aggregation with Automated Market Makers

Computational Economics, Forthcoming

28 Pages Posted: 11 Jul 2013 Last revised: 26 Sep 2015

See all articles by Rajiv Sethi

Rajiv Sethi

Barnard College, Columbia University; Santa Fe Institute

Jennifer Vaughan

Microsoft Research New York City

Date Written: June 3, 2015


We consider the properties of a cost function based automated market maker aggregating the beliefs of risk-averse traders with finite budgets. Individuals can interact with the market maker an arbitrary number of times before the state of the world is revealed. We show that the resulting sequence of prices offered by the market maker is convergent under general conditions, and explore the properties of the limiting price and trader portfolios. The limiting price cannot be expressed as a function of trader beliefs, since it is sensitive to the market maker's cost function as well as the order in which traders interact with the market. For a range of trader preferences, however, we show numerically that the limiting price provides a good approximation to a weighted average of beliefs, inclusive of the market designer's prior belief as reflected in the initial contract price. This average is computed by weighting trader beliefs by their respective budgets, and weighting the initial contract price by the market maker's worst-case loss, implicit in the cost function. Since cost function parameters are chosen by the market designer, this allows for an inference regarding the budget-weighted average of trader beliefs.

Keywords: Prediction Markets, Market Scoring Rules, Automated Market Makers

JEL Classification: D84, G13

Suggested Citation

Sethi, Rajiv and Vaughan, Jennifer, Belief Aggregation with Automated Market Makers (June 3, 2015). Computational Economics, Forthcoming, Available at SSRN: or

Rajiv Sethi (Contact Author)

Barnard College, Columbia University ( email )

3009 Broadway
New York, NY 10027
United States
212-854-5140 (Phone)


Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Jennifer Vaughan

Microsoft Research New York City ( email )

641 Avenue of Americas
New York, NY 10011
United States

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