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26
A new understanding of prediction markets via noregret learning
 In ACM EC
, 2010
"... We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and noregret 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 ..."
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Cited by 30 (10 self)
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We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and noregret 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 ( √ 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.
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
Bluffing and strategic reticence in prediction markets
 In the third Workshop on Internet and Network Economics
, 2007
"... Abstract. We study the equilibrium behavior of informed traders interacting with two types of automated market makers: market scoring rules (MSR) and dynamic parimutuel markets (DPM). Although both MSR and DPM subsidize trade to encourage information aggregation, and MSR is myopically incentive comp ..."
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Cited by 12 (6 self)
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Abstract. We study the equilibrium behavior of informed traders interacting with two types of automated market makers: market scoring rules (MSR) and dynamic parimutuel markets (DPM). Although both MSR and DPM subsidize trade to encourage information aggregation, and MSR is myopically incentive compatible, neither mechanism is incentive compatible in general. That is, there exist circumstances when traders can benefit by either hiding information (reticence) or lying about information (bluffing). We examine what information structures lead to straightforward play by traders, meaning that traders reveal all of their information truthfully as soon as they are able. Specifically, we analyze the behavior of riskneutral traders with incomplete information playing in a finiteperiod dynamic game. We employ two different information structures for the logarithmic market scoring rule (LMSR): conditionally independent signals and conditionally dependent signals. When signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE) for LMSR. However, when signals are conditionally dependent, there exist joint probability distributions on signals such that at a PBE in LMSR traders have an incentive to bet against their own information—strategically misleading other traders in order to later profit by correcting their errors. In DPM, we show that when traders anticipate sufficiently betterinformed traders entering the market in the future, they have incentive to partially withhold their information by moving the market probability only partway toward their beliefs, or in some cases not participating in the market at all. 1
Prediction Mechanisms That Do Not Incentivize Undesirable Actions
 In WINE
, 2009
"... Abstract. A potential downside of prediction markets is that they may incentivize agents to take undesirable actions in the real world. For example, a prediction market for whether a terrorist attack will happen may incentivize terrorism, and an inhouse prediction market for whether a product will ..."
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Cited by 11 (1 self)
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Abstract. A potential downside of prediction markets is that they may incentivize agents to take undesirable actions in the real world. For example, a prediction market for whether a terrorist attack will happen may incentivize terrorism, and an inhouse prediction market for whether a product will be successfully released may incentivize sabotage. In this paper, we study principalaligned prediction mechanisms– mechanisms that do not incentivize undesirable actions. We characterize all principalaligned proper scoring rules, and we show an “overpayment” result, which roughly states that with n agents, any prediction mechanism that is principalaligned will, in the worst case, require the principal to pay Θ(n) times as much as a mechanism that is not. We extend our model to allow uncertainties about the principal’s utility and restrictions on agents ’ actions, showing a richer characterization and a similar “overpayment ” result.
Mechanism Design on Trust Networks
"... Abstract. We introduce the concept of a trust network—a decentralized payment infrastructure in which payments are routed as IOUs between trusted entities. The trust network has directed links between pairs of agents, with capacities that are related to the credit an agent is willing to extend anoth ..."
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Cited by 10 (1 self)
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Abstract. We introduce the concept of a trust network—a decentralized payment infrastructure in which payments are routed as IOUs between trusted entities. The trust network has directed links between pairs of agents, with capacities that are related to the credit an agent is willing to extend another; payments may be routed between any two agents that are connected by a path in the network. The network structure introduces group budget constraints on the payments from a subset of agents to another on the trust network: this generalizes the notion of individually budget constrained bidders. We consider a multiunit auction of identical items among bidders with unit demand, when the auctioneer and bidders are all nodes on a trust network. We define a generalized notion of social welfare for such budgetconstrained bidders, and show that the winner determination problem under this notion of social welfare is NPhard; however the flow structure in a trust network can be exploited to approximate the solution with a factor of 1 − 1/e. We then present a pricing scheme that leads to an incentive compatible, individually rational mechanism with feasible payments that respect the trust network’s payment constraints and that maximizes the modified social welfare to within a factor 1 − 1/e. 1
Parimutuel Markets: Mechanisms and Performance
, 2008
"... Recently, there has been an increase in the usage of centrally managed markets which are run by some form of parimutuel mechanism. A parimutuel mechanism is characterized by the ability to shield the market organizer from financial risk by paying the winners from the stakes of the losers. The recen ..."
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Cited by 9 (3 self)
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Recently, there has been an increase in the usage of centrally managed markets which are run by some form of parimutuel mechanism. A parimutuel mechanism is characterized by the ability to shield the market organizer from financial risk by paying the winners from the stakes of the losers. The recent introduction of new, modified parimutuel methods has spurred the growth of prediction markets as well as new financial derivative markets. Coinciding with this increased usage, there has been much work on the research front which has produced several mechanisms and a slew of interesting results. We will introduce a new parimutuel marketmaker mechanism with many positive qualities including convexity, truthfulness and strong performance. Additionally, we will provide the first quantitative performance comparison of some of the existing parimutuel marketmaker mechanisms. 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 8 (7 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.
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
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