I develop a new mechanism for risk allocation and information speculation called a dynamic pari-mutuel market (DPM). A DPM acts as hybrid between a pari-mutuel market and a continuous double auction (CDA), inheriting some of the advantages of both. Like a pari-mutuel market, a DPM offers infinite buy-in liquidity and zero risk for the market institution; like a CDA, a DPM can continuously react to new information, dynamically incorporate information into prices, and allow traders to lock in gains or limit losses by selling prior to event resolution. The trader interface can be designed to mimic the familiar double auction format with bid-ask queues, though with an addition variable called the payoff per share. The DPM price function can be viewed as an automated market maker always offering to sell at some price, and moving the price appropriately according to demand. Since the mechanism is pari-mutuel (i.e., redistributive), it is guaranteed to pay out exactly the amount of money taken in. I explore a number of variations on the basic DPM, analyzing the properties of each, and solving in closed form for their respective price functions.

We analyze data from $52$ online in-game sports betting markets (where betting is allowed continuously throughout a game), including 34 markets based on soccer (European football) games from the 2002 World Cup, and 18 basketball games from the 2002 USA National Basketball Association (NBA) championship. We show that prices on average approach the correct outcome over time, and the price dynamics in the markets are closely coupled with game events, agreeing with efficient market assumptions. We also examine qualitative distinctions between the two types of games.

Game sites on the World Wide Web draw people from around the world with specialized interests, skills, and knowledge.

We develop a framework for trading in compound securities: financial instruments that pay off contingent on the outcomes of arbitrary statements in propositional logic. Buying or selling securities -- which can be thought of as betting on or against a particular future outcome -- allows agents both to hedge risk and to profit (in expectation) on subjective predictions. A compound securities market allows agents to place bets on arbitrary boolean combinations of events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole to more closely achieve the social optimum. The tradeoff for allowing such expressivity is in the complexity of the agents' and auctioneer's optimization problems.

According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information distributed among traders is revealed stepby -step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as a weighted threshold function of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.

We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson’s popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We examine both permutation combinatorics, where outcomes are permutations of objects, and Boolean combinatorics, where outcomes are combinations of binary events. We look at three restrictive languages that limit what traders can bet on. Even with severely limited languages, we find that LMSR pricing is #P-hard, even when the same language admits polynomial-time matching without the market maker. We then propose an approximation technique for pricing permutation markets based on a recent algorithm for online permutation learning. The connections we draw between LMSR pricing and the vast literature on online learning with expert advice may be of independent interest.

Interest in prediction markets has increased in the last decade, driven in part by the hope that these markets will prove to be valuable tools in forecasting, decisionmaking and risk management – in both the public and private sectors. This paper outlines five open questions in the literature, and we argue that resolving these questions is crucial to determining whether current optimism about prediction markets will be realized.

The favorite-longshot bias presents a challenge for theories of decision making under uncertainty. This longstanding empirical regularity is that betting odds provide biased estimates of the probability of a horse winning—longshots are overbet, while favorites are underbet. Neoclassical explanations focus on rational gamblers who overbet longshots due to risk-love. The competing behavioral explanations emphasize the role of misperceptions of probabilities. We provide novel empirical tests that can discriminate between these competing theories by focusing on the pricing of compound bets. We test whether the models that explain gamblers ’ choices in one part of their choice set (betting to win) can also rationalize decisions over a wider choice set, including compound bets in the exacta, quinella or trifecta pools. Using a new, large-scale dataset ideally suited to implement these tests we find evidence in favor of the view that misperceptions of probability drive the favorite-longshot bias, as suggested by Prospect Theory. Along the way we provide more robust evidence on the favorite-longshot bias, falsifying the conventional wisdom that the bias is large enough to yield profit opportunities (it isn’t) and that it becomes more severe in the last race (it doesn’t). ∗We thank David Siegel of Equibase for supplying the data, and Scott Hereld and Ravi Pillai for their

We examine a class of wagering mechanisms designed to elicit truthful predictions from a group of people without requiring any outside subsidy. We propose a number of desirable properties for wagering mechanisms, identifying one mechanism—weighted-score wagering—that satisfies all of the properties. Moreover, we show that a single-parameter generalization of weighted-score wagering is the only mechanism that satisfies these properties. We explore some variants of the core mechanism based on practical considerations. Categories and Subject Descriptors

We develop a model of how information flows into a market, and derive algorithms for automatically detecting and explaining relevant events. We analyze data from twenty-two "political stock markets" (i.e., betting markets on political outcomes) on the Iowa Electronic Market (IEM). We prove that, under certain eciency assumptions, prices in such betting markets will on average approach the correct outcomes over time, and show that IEM data conforms closely to the theory. We present a simple model of a betting market where information is revealed over time, and show a qualitative correspondence between the model and real market data. We also present an algorithm for automatically detecting significant events and generating semantic explanations of their origin. The algorithm operates by discovering significant changes in vocabulary on online news sources (using expected entropy loss) that align with major price spikes in related betting markets.