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An OptimizationBased Framework for Automated MarketMaking
 EC'11
, 2011
"... We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any ..."
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Cited by 23 (11 self)
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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomialtime pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget.
Designing Markets for Prediction
, 2010
"... We survey the literature on prediction mechanisms, including prediction markets and peer prediction systems. We pay particular attention to the design process, highlighting the objectives and properties that are important in the design of good prediction mechanisms. ..."
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Cited by 20 (3 self)
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We survey the literature on prediction mechanisms, including prediction markets and peer prediction systems. We pay particular attention to the design process, highlighting the objectives and properties that are important in the design of good prediction mechanisms.
Efficient market making via convex optimization, and a connection to online learning
 ACM Transactions on Economics and Computation. To Appear
, 2012
"... We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any ..."
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Cited by 19 (9 self)
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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomialtime pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget. Although our framework was designed with the goal of deriving efficient automated market makers for markets with very large outcome spaces, this framework also provides new insights into the relationship between market design and machine learning, and into the complete market setting. Using our framework, we illustrate the mathematical parallels between cost function based markets and online learning and establish a correspondence between cost function based markets and market scoring rules for complete markets. 1
Betting on the Real Line
"... Abstract. 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 mech ..."
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Cited by 10 (8 self)
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Abstract. 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 continuousoutcome 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.
FourierInformation Duality in the Identity Management Problem
"... Abstract. We compare two recently proposed approaches for representing probability distributions over the space of permutations in the context of multitarget tracking. We show that these two representations, the Fourier approximation and the information form approximation can both be viewed as low ..."
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Cited by 1 (0 self)
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Abstract. We compare two recently proposed approaches for representing probability distributions over the space of permutations in the context of multitarget tracking. We show that these two representations, the Fourier approximation and the information form approximation can both be viewed as low dimensional projections of a true distribution, but with respect to different metrics. We identify the strengths and weaknesses of each approximation, and propose an algorithm for converting between the two forms, allowing for a hybrid approach that draws on the strengths of both representations. We show experimental evidence that there are situations where hybrid algorithms are favorable. 1
Applied Sciences Harvard University
"... We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any ..."
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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomialtime pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget.
Proceedings Article Cost Function Market Makers for Measurable Spaces
"... We characterize cost function market makers designed to elicit traders ’ beliefs about the expectations of an infinite set of random variables or the full distribution of a continuous random variable. This characterization is derived from a duality perspective that associates the market maker’s liab ..."
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We characterize cost function market makers designed to elicit traders ’ beliefs about the expectations of an infinite set of random variables or the full distribution of a continuous random variable. This characterization is derived from a duality perspective that associates the market maker’s liabilities with market beliefs, generalizing the framework of Abernethy et al. [2011, 2013], but relies on a new subdifferential analysis. It differs from prior approaches in that it allows arbitrary market beliefs, not just those that admit density functions. This allows us to overcome the impossibility results of Gao and Chen [2010] and design the first automated market maker for betting on the realization of a continuous random variable taking values in [0, 1] that has bounded loss without resorting to discretization. Additionally, we show that scoring rules are derived from the same duality and share a close connection with cost functions for eliciting beliefs.
Advances in Ranking
"... Ranking problems are increasingly recognized as a new class of statistical learning problems that are distinct from the classical learning problems of classification and regression. Such problems arise in a wide variety of domains, such as information retrieval, natural language processing, collabor ..."
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Ranking problems are increasingly recognized as a new class of statistical learning problems that are distinct from the classical learning problems of classification and regression. Such problems arise in a wide variety of domains, such as information retrieval, natural language processing, collaborative filtering, and computational biology. Consequently, there has been increasing interest in ranking in recent years, with a variety of methods being developed and a whole host of new applications being discovered. This workshop brings together researchers interested in the area to share their perspectives, identify persisting challenges as well as opportunities for meaningful dialogue and collaboration, and to discuss possible directions for further advances and applications in the future. The workshop web site is: