Multi-outcome and Multidimensional Market Scoring Rules

Hanson's market scoring rules allow us to design a prediction market that still gives useful information even if we have an illiquid market with a limited number of budget-constrained agents. Each agent can "move" the current price of a market towards their prediction. While this movement still occurs in multi-outcome or multidimensional markets we show that no market-scoring rule, under reasonable conditions, always moves the price directly towards beliefs of the agents. We present a modified version of a market scoring rule for budget-limited traders, and show that it does have the property that, from any starting position, optimal trade by a budget-limited trader will result in the market being moved towards the trader's true belief. This mechanism also retains several attractive strategic properties of the market scoring rule

Budget constraints in prediction markets

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, e give sufficient conditions for a property we call budget additivity: two traders with budgets B and B0 and the same beliefs would have a combined impact equal to a single trader with budget B +B0. 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.postprin

All Men Count with You, but None Too Much: Information Aggregation and Learning in Prediction Markets.

Prediction markets are markets that are set up to aggregate information from a population of traders in order to predict the outcome of an event. In this thesis, we consider the problem of designing prediction markets with discernible semantics of aggregation whose syntax is amenable to analysis. For this, we will use tools from computer science (in particular, machine learning), statistics and economics. First, we construct generalized log scoring rules for outcomes drawn from high-dimensional spaces. Next, based on this class of scoring rules, we design the class of exponential family prediction markets. We show that this market mechanism performs an aggregation of private beliefs of traders under various agent models. Finally, we present preliminary results extending this work to understand the dynamics of related markets using probabilistic graphical model techniques. We also consider the problem in reverse: using prediction markets to design machine learning algorithms. In particular, we use the idea of sequential aggregation from prediction markets to design machine learning algorithms that are suited to situations where data arrives sequentially. We focus on the design of algorithms for recommender systems that are robust against cloning attacks and that are guaranteed to perform well even when data is only partially available.PHDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111398/1/skutty_1.pd