Betting on the Real Line

We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mechanisms, logarithmic market scoring rule (LMSR) and dynamic parimutuel markets (DPM), are generalized to handle interval bets on continuous or countably infinite outcomes. We examine problems associated with operating these markets. We show that the auctioneer's order matching problem for interval bets can be solved in polynomial time for call markets. DPM can be generalized to deal with interval bets on both countably infinite and continuous outcomes and remains to have bounded loss. However, in a continuous-outcome DPM, a trader may incur loss even if the true outcome is within her betting interval. The LMSR market maker suffers from unbounded loss for both countably infinite and continuous outcomes.Engineering and Applied Science

Monopoly rents and price fixing in betting markets

Betting markets provide an ideal environment in which to examine monopoly power due to the availability of detailed information on product pricing. In this paper we argue that the pricing strategies of companies in the UK betting industry are likely to be an important source of monopoly rents, particularly in the market for forecast bets. Pricing in these markets are shown to be explicitly coordinated. Further, price information is asymmetrically biased in favor of producers. We find evidence, based on UK data, that pricing of CSF bets is characterized by a significantly higher markup than pricing of single bets. Although this differential can in part be explained by the preferences of bettors, it is reasonable to attribute a significant part of the differential as being due to monopoly power

A New Understanding of Prediction Markets Via No-Regret Learning

We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We first show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating the set of outcomes on which bets are placed in the market with the set of experts in the learning setting, and equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an $O( \sqrt T)$ regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies both that any market scoring rule can be implemented as a cost function based market maker, and that market scoring rules can be interpreted naturally as Follow the Regularized Leader algorithms. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.Engineering and Applied Science

The racetrack : a scientific approach

Includes bibliographical references.Horseracing and its associated activity of gambling invites academic research of a multidisciplinary nature. Economics, psychology, mathematics and statistics are all fields that have investigated the two topics. In 1976 economists discovered a new body of data on which they could test their theories. For many years psychologists have investigated human behaviour in gambling situations. Mathematicians have developed optimal betting strategies. Statisticians have assisted in all the investigations as well as utilised decision theory, probability theory and regression analysis, in their own right, within the discipline. Why do academics devote their time to this subject? The furthering of knowledge in general in the above fields is important. Also, because the possibility of making money with relatively little work exists, people from all walks of life will be drawn to the intellectual challenge of finding winners. Researchers know that in order to derive money making systems, research on an academic scale is necessary. The amount of data available is phenomenal and although much of it is utilized by the public, some of it is not and that which is, is not always used in a consistent manner. The research in this work concentrates on all four fields mentioned above. A general, overview of the work done in each section is as follows. In chapters two and three, the betting market is examined within the framework of the efficient markets hypothesis. Tests of the three well known forms of efficiency are performed. In chapter four, within the framework of the expected utility hypothesis, the behaviour of gamblers is analysed. The investigation concentrates on behaviour observed at the racetrack, but draws ideas from other gambling situations as well. In chapter five, an investigation is made into horseraces, considering a race to be a sports event. This will consider the competing horses as athletes and will try and identify which fundamental factors are most important in determining the victor of such a race. In chapter six, some statistical theory, which has simple applications in horseracing is examined. In chapter seven, the economics of racetrack management is investigated

Entropy-Based Strategies for Multi-Bracket Pools

Much work in the March Madness literature has discussed how to estimate the probability that any one team beats any other team. There has been strikingly little work, however, on what to do with these win probabilities. Hence we pose the multi-brackets problem: given these probabilities, what is the best way to submit a set of $n$ brackets to a March Madness bracket challenge? This is an extremely difficult question, so we begin with a simpler situation. In particular, we compare various sets of $n$ randomly sampled brackets, subject to different entropy ranges or levels of chalkiness (rougly, chalkier brackets feature fewer upsets). We learn three lessons. First, the observed NCAA tournament is a "typical" bracket with a certain "right" amount of entropy (roughly, a "right" amount of upsets), not a chalky bracket. Second, to maximize the expected score of a set of $n$ randomly sampled brackets, we should be successively less chalky as the number of submitted brackets increases. Third, to maximize the probability of winning a bracket challenge against a field of opposing brackets, we should tailor the chalkiness of our brackets to the chalkiness of our opponents' brackets

Prediction Markets:A literature review 2014

In recent years, Prediction Markets gained growing interest as a forecasting tool among researchers as well as practitioners, which resulted in an increasing number of publications. In order to track the latest development of research, comprising the extent and focus of research, this article provides a comprehensive review and classification of the literature related to the topic of Prediction Markets. Overall, 304 relevant articles, published in the timeframe from 2007 through 2013, were identified and assigned to a herein presented classification scheme, differentiating between descriptive works, articles of theoretical nature, application-oriented studies and articles dealing with the topic of law and policy. The analysis of the research results reveals that more than half of the literature pool deals with the application and actual function tests of Prediction Markets. The results are further compared to two previous works published by Zhao, Wagner and Chen (2008) and Tziralis and Tatsiopoulos (2007a). The article concludes with an extended bibliography section and may therefore serve as a guidance and basis for further research. (250 WORDS

An introduction to complete markets

Markets

A review on Estimation of Distribution Algorithms in Permutation-based Combinatorial Optimization Problems

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. Characterized by the use of probabilistic models to represent the solutions and the dependencies between the variables of the problem, these algorithms have been applied to a wide set of academic and real-world optimization problems, achieving competitive results in most scenarios. Nevertheless, there are some optimization problems, whose solutions can be naturally represented as permutations, for which EDAs have not been extensively developed. Although some work has been carried out in this direction, most of the approaches are adaptations of EDAs designed for problems based on integer or real domains, and only a few algorithms have been specifically designed to deal with permutation-based problems. In order to set the basis for a development of EDAs in permutation-based problems similar to that which occurred in other optimization fields (integer and real-value problems), in this paper we carry out a thorough review of state-of-the-art EDAs applied to permutation-based problems. Furthermore, we provide some ideas on probabilistic modeling over permutation spaces that could inspire the researchers of EDAs to design new approaches for these kinds of problems