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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 14 (6 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.
Articles Designing Markets for Prediction
"... � 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. Mechanism design has been descr ..."
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Cited by 13 (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. Mechanism design has been described as “inverse game theory. ” Whereas game theorists ask what outcome results from a game, mechanism designers ask what game produces a desired outcome. In this sense, game theorists act like scientists and mechanism designers like engineers. In this article, we survey a number of mechanisms created to elicit predictions, many newly proposed within the last decade. We focus on the engineering questions: How do they work and why? What factors and goals are most important in their
Selffinanced wagering mechanisms for forecasting
 EC
"... 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—weightedscore wagering—that satisfies all of the properties. ..."
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Cited by 11 (5 self)
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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—weightedscore wagering—that satisfies all of the properties. Moreover, we show that a singleparameter generalization of weightedscore 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
Parimutuel betting on permutations
 In International Workshop on Internet and Network Economics
, 2008
"... We focus on a permutation betting market under parimutuel call auction model where traders bet on the final ranking of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows the traders to bet on any subset of the n 2 ‘candidaterank ’ pairs, and rewards them ..."
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Cited by 8 (0 self)
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We focus on a permutation betting market under parimutuel call auction model where traders bet on the final ranking of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows the traders to bet on any subset of the n 2 ‘candidaterank ’ pairs, and rewards them proportionally to the number of pairs that appear in the final outcome. We show that market organizer’s decision problem for this mechanism can be formulated as a convex program of polynomial size. More importantly, the formulation yields a set of n 2 unique marginal prices that are sufficient to price the bets in this mechanism, and are computable in polynomialtime. The marginal prices reflect the traders ’ beliefs about the marginal distributions over outcomes. We also propose techniques to compute the joint distribution over n! permutations from these marginal distributions. We show that using a maximum entropy criterion, we can obtain a concise parametric form (with only n 2 parameters) for the joint distribution which is defined over an exponentially large state space. We then present an approximation algorithm for computing the parameters of this distribution. In fact, the algorithm addresses the generic problem of finding the maximum entropy distribution over permutations that has a given mean, and may be of independent interest. 1
A Unified Framework for Dynamic Prediction Market Design
"... Recently, coinciding with and perhaps driving the increased popularity of prediction markets, several novel parimutuel mechanisms have been developed such as the logarithmic market scoring rule (LMSR), the costfunction formulation of market makers, utilitybased markets, and the sequential convex ..."
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Cited by 6 (1 self)
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Recently, coinciding with and perhaps driving the increased popularity of prediction markets, several novel parimutuel mechanisms have been developed such as the logarithmic market scoring rule (LMSR), the costfunction formulation of market makers, utilitybased markets, and the sequential convex parimutuel mechanism (SCPM). In this work, we present a convex optimization framework which unifies these seemingly unrelated models for centrally organizing contingent claims markets. The existing mechanisms can be expressed in our unified framework by varying the choice of a concave value function. We show that this framework is equivalent to a convex risk minimization model for the market maker. This facilitates a better understanding of the risk attitudes adopted by various mechanisms. The unified framework also leads to easy implementation since we can now find the cost function of a market maker in polynomial time by solving a simple convex optimization problem. In addition to unifying and explaining the existing mechanisms, we use the generalized framework to derive necessary and sufficient conditions for many desirable properties of a prediction market mechanism such as proper scoring, truthful bidding (in a myopic sense), efficient computation, controllable riskmeasure, and guarantees on the worstcase loss. As a result, we develop the first proper, truthful, risk controlled, lossbounded (in number of states) mechanism; none of the previously proposed mechanisms possessed all
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 5 (2 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
An Axiomatic Characterization of ContinuousOutcome Market Makers
, 2010
"... Most existing market maker mechanisms for prediction markets are designed for events with a finite number of outcomes. All known attempts on designing market makers for forecasting continuousoutcome events resulted in mechanisms with undesirable properties. In this paper, we take an axiomatic appr ..."
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Cited by 1 (1 self)
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Most existing market maker mechanisms for prediction markets are designed for events with a finite number of outcomes. All known attempts on designing market makers for forecasting continuousoutcome events resulted in mechanisms with undesirable properties. In this paper, we take an axiomatic approach to study whether it is possible for continuousoutcome market makers to satisfy certain desirable properties simultaneously. We define a general class of continuousoutcome market makers, which allows traders to express their information on any continuous subspace of their choice. We characterize desirable properties of these market makers using formal axioms. Our main result is an impossibility theorem showing that if a market maker offers binarypayoff contracts, either the market maker has unbounded worst case loss or the contract prices will stop being responsive, making future trades no longer profitable. In addition, we analyze a mechanism that does not belong to our framework. This mechanism has a worst case loss linear in the number of submitted orders, but encourages some undesirable strategic behavior.
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 ..."
Abstract
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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.