Information Aggregation in Exponential Family Markets

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship and explore a range of benefits. We draw connections between the information aggregation of market prices and the belief aggregation of learning agents that rely on exponential family distributions. We develop a very natural analysis of the market behavior as well as the price equilibrium under the assumption that the traders exhibit risk aversion according to exponential utility. We also consider similar aspects under alternative models, such as when traders are budget constrained

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

Essays in Corporate Prediction Markets

Personal subjective opinions are one of the most important assets in management. Prediction markets are mechanisms that can be deployed to elicit and aggregate a group of people’s opinions regarding the outcome of future events at any point in time. Prediction markets are exchange-traded markets where security values are tied to the outcome of future events. Prediction markets are systematically designed in a way that their market prices capture the crowd’s consensus about the probability of a future event. Corporations harness internal prediction markets for managerial decision making and business forecasting. Prediction markets are traditionally designed for large and diverse populations, two properties that are not often displayed in corporate settings. Therefore special considerations must be given to prediction markets used in corporations. Our first contribution in this thesis is in addressing the issue of diversity, in the sense of risk preferences, in corporate prediction markets. We study prediction markets in the presence of risk averse or risk seeking agents that have unknown risk preferences. We show that such agents’ behavior is not desirable for the purpose of information aggregation. We then characterize the agents’ behavior with respect to prediction market parameters and offer a systematic method to market organizers that fine tunes market parameters so at to best mitigate the impact of a pool agents’ risk-preferences. Our Second contribution in this thesis is in recommending prediction market mechanisms in different settings. There are many prediction market mechanisms with various advantages and weaknesses. The choice of a market mechanism can heavily affect the market accuracy and in turn, the success of a managerial decision, or a forecast based on prediction markets’ prices. Using trade data from two real-world prediction markets, we study the two main types of prediction markets mechanism and provide the much-needed insight as to what market mechanism to choose in various situations

Prediction Markets for Machine Learning: Equilibrium Behaviour through Sequential Markets

Prediction markets which trade on contracts representing unknown future outcomes are designed specifically to aggregate expert predictions via the market price. While there are some existing machine learning interpretations for the market price and connections to Bayesian updating under the equilibrium analysis of such markets, there is less of an understanding of what the instantaneous price in sequentially traded markets means. In this thesis I show that the prices generated in sequentially traded prediction markets are stochastic approximations to the price given by an equilibrium analysis. This is done by showing that the equilibrium price is a solution to a stochastic optimisation problem which is solved by stochastic mirror descent (SMD) by a class of sequential pricing mechanisms. This connection leads to proposing a scheme called “mini-trading” which introduces a parameter related to the learning rate in SMD. I prove several properties of this scheme and show that it can improve the stability of prices in sequentially traded prediction markets. Also I analyse two popular trading models (namely the Maximum Expected Utility model and the Risk-measure model) in respect to an assumption on the class of traders I required to interpret sequential markets as SMD. I derive a sufficient condition for when the Maximum Expected Utility traders satisfy this assumption, but show that risk-measure based traders naturally satisfy this assumption for the type of markets I consider. Then I show that the “regret” of mini-trading markets (with respect to equilibrium markets) depend on the mini-trade parameter. Finally I attempt to compare the wealth updates of traders in sequential markets to the wealth updates in equilibrium markets, since this would help to extend the interpretation of equilibrium markets as performing Bayesian updates to sequential markets. For this I present preliminary results