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29
An empirical comparison of algorithms for aggregating expert predictions
 In UAI
, 2006
"... Predicting the outcomes of future events is a challenging problem for which a variety of solution methods have been explored and attempted. We present an empirical comparison of a variety of online and offline adaptive algorithms for aggregating experts ’ predictions of the outcomes of five years of ..."
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Cited by 16 (5 self)
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Predicting the outcomes of future events is a challenging problem for which a variety of solution methods have been explored and attempted. We present an empirical comparison of a variety of online and offline adaptive algorithms for aggregating experts ’ predictions of the outcomes of five years of US National Football League games (1319 games) using expert probability elicitations obtained from an Internet contest called ProbabilitySports. We find that it is difficult to improve over simple averaging of the predictions in terms of prediction accuracy, but that there is room for improvement in quadratic loss. Somewhat surprisingly, a Bayesian estimation algorithm which estimates the variance of each expert’s prediction exhibits the most consistent superior performance over simple averaging among our collection of algorithms. 1
Adapting to a Market Shock: Optimal Sequential MarketMaking
"... We study the profitmaximization problem of a monopolistic marketmaker who sets twosided prices in an asset market. The sequential decision problem is hard to solve because the state space is a function. We demonstrate that the belief state is well approximated by a Gaussian distribution. We prove ..."
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Cited by 16 (4 self)
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We study the profitmaximization problem of a monopolistic marketmaker who sets twosided prices in an asset market. The sequential decision problem is hard to solve because the state space is a function. We demonstrate that the belief state is well approximated by a Gaussian distribution. We prove a key monotonicity property of the Gaussian state update which makes the problem tractable, yielding the first optimal sequential marketmaking algorithm in an established model. The algorithm leads to a surprising insight: an optimal monopolist can provide more liquidity than perfectly competitive marketmakers in periods of extreme uncertainty, because a monopolist is willing to absorb initial losses in order to learn a new valuation rapidly so she can extract higher profits later. 1
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
Eliciting Honest Reputation Feedback in a Markov Setting
"... Recently, online reputation mechanisms have been proposed that reward agents for honest feedback about products and services with fixed quality. Many realworld settings, however, are inherently dynamic. As an example, consider a web service that wishes to publish the expected download speed of a fi ..."
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Cited by 7 (6 self)
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Recently, online reputation mechanisms have been proposed that reward agents for honest feedback about products and services with fixed quality. Many realworld settings, however, are inherently dynamic. As an example, consider a web service that wishes to publish the expected download speed of a file mirrored on different server sites. In contrast to the models of Miller, Resnick and Zeckhauser and of Jurca and Faltings, the quality of the service (e. g., a server’s available bandwidth) changes over time and future agents are solely interested in the present quality levels. We show that hidden Markov models (HMM) provide natural generalizations of these static models and design a payment scheme that elicits honest reports from the agents after they have experienced the quality of the service. 1
Composition of Markets with Conflicting Incentives
"... We study information revelation in scoring rule and prediction market mechanisms in settings in which traders have conflicting incentives due to opportunities to profit from the market operator’s subsequent actions. In our canonical model, an agent Alice is offered an incentivecompatible scoring ru ..."
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Cited by 6 (0 self)
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We study information revelation in scoring rule and prediction market mechanisms in settings in which traders have conflicting incentives due to opportunities to profit from the market operator’s subsequent actions. In our canonical model, an agent Alice is offered an incentivecompatible scoring rule to reveal her beliefs about a future event, but can also profit from misleading another trader Bob about her information and then making money off Bob’s error in a subsequent market. We show that, in any weak Perfect Bayesian Equilibrium of this sequence of two markets, Alice and Bob earn payoffs that are consistent with a minimax strategy of a related game. We can then characterize the equilibria in terms of an information channel: the outcome of the first scoring rule is as if Alice had only observed a noisy version of her initial signal, with the degree of noise indicating the adverse effect of the second market on the first. We provide a partial constructive characterization of when this channel will be noiseless. We show that our results on the canonical model yield insights into other settings of information extraction with conflicting incentives.
Comparing Prediction Market Structures, With an Application to Market Making
, 1009
"... Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Various market making algorithms have been proposed in the literature and deployed in practice, but there has been little effort to evaluate their benefits and disadvantages in a systematic manner. We int ..."
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Cited by 5 (0 self)
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Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Various market making algorithms have been proposed in the literature and deployed in practice, but there has been little effort to evaluate their benefits and disadvantages in a systematic manner. We introduce a novel experimental design for comparing market structures in live trading that ensures fair comparison between two different microstructures with the same trading population. Participants trade on outcomes related to a twodimensional random walk that they observe on their computer screens. They can simultaneously trade in two markets, corresponding to the independent horizontal and vertical random walks. We use this experimental design to compare the popular inventorybased logarithmic market scoring rule (LMSR) market maker and a new information based Bayesian market maker (BMM). Our experiments reveal that BMM can offer significant benefits in terms of price stability and expected loss when controlling for liquidity; the caveat is that, unlike LMSR, BMM does not guarantee bounded loss. Our investigation also elucidates some general properties of market makers in prediction markets. In particular, there is an inherent tradeoff between adaptability to market shocks and convergence during market equilibrium. 1
Aggregation of information and beliefs in prediction markets. FRU Working Papers
, 2007
"... We propose a simple model of prediction markets in which traders with heterogeneous prior beliefs and private information are allowed to risk a limited amount of money. For any given information realization, the equilibrium price can be interpreted as a posterior belief given a representative market ..."
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We propose a simple model of prediction markets in which traders with heterogeneous prior beliefs and private information are allowed to risk a limited amount of money. For any given information realization, the equilibrium price can be interpreted as a posterior belief given a representative market prior belief. However, across information realizations, we show that this market prior belief is a decreasing function of the likelihood ratio of the private information possessed by the traders. Thus, the market price underreacts to information, consistent with the favoritelongshot bias. Underreaction results more generally under the realistic assumption that traders have decreasing absolute risk aversion.
Rational Expectations at the Racetrack: Testing Expected Utility Using Prediction Market Prices.” University of WisconsinMadison, mimeo
, 2007
"... Empirical studies have cast doubt on one of the bedrocks of applied economic modeling the expected utility hypothesis. Economists have documented pricing anomalies, like the longshot bias in prediction markets (low probability events are priced too high), that are inconsistent with classical repre ..."
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Cited by 4 (0 self)
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Empirical studies have cast doubt on one of the bedrocks of applied economic modeling the expected utility hypothesis. Economists have documented pricing anomalies, like the longshot bias in prediction markets (low probability events are priced too high), that are inconsistent with classical representative agent models. In this paper, we show that the inconsistency is due to the representative agent assumption, and not to the expected utility hypothesis. When agents differ in their information sets and risk preferences, we show that trader heterogeneity can easily explain the observed pattern of price variation across betting and prediction markets. In particular, the long shot bias is found to be due to a group of traders, whom we dub the “riskaverting grandmas”, who make up about 40 percent of the trading group and bet on the top favorite in a race in exchange for a premium. We show also that the expected utility hypothesis outperforms the main “behavioral” alternatives, rank dependent expected utility, and cumulative prospect theory.
Prediction Markets, Mechanism Design, and Cooperative Game Theory
"... Prediction markets are designed to elicit information from multiple agents in order to predict (obtain probabilities for) future events. A good prediction market incentivizes agents to reveal their information truthfully; such incentive compatibility considerations are commonly studied in mechanism ..."
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Cited by 3 (2 self)
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Prediction markets are designed to elicit information from multiple agents in order to predict (obtain probabilities for) future events. A good prediction market incentivizes agents to reveal their information truthfully; such incentive compatibility considerations are commonly studied in mechanism design. While this relation between prediction markets and mechanism design is well understood at a high level, the models used in prediction markets tend to be somewhat different from those used in mechanism design. This paper considers a model for prediction markets that fits more straightforwardly into the mechanism design framework. We consider a number of mechanisms within this model, all based on proper scoring rules. We discuss basic properties of these mechanisms, such as incentive compatibility. We also draw connections between some of these mechanisms and cooperative game theory. Finally, we speculate how one might build a practical prediction market based on some of these ideas. 1
PARTITIONDEPENDENT FRAMING EFFECTS IN LAB AND FIELD PREDICTION MARKETS*
"... Many psychology experiments show that individually judged probabilities of the same event can vary depending on the partition of the state space (a framing effect called "partitiondependence"). We show that these biases transfer to competitive prediction markets in which multiple informed ..."
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Cited by 1 (1 self)
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Many psychology experiments show that individually judged probabilities of the same event can vary depending on the partition of the state space (a framing effect called "partitiondependence"). We show that these biases transfer to competitive prediction markets in which multiple informed traders are provided economic incentives to bet on their beliefs about events. We report results of a short controlled lab study, a longer field experiment (betting on the NBA playoffs and the FIFA World Cup), and naturallyoccurring trading in macroeconomic derivatives. The combined evidence suggests that partitiondependence can exist and persist in lab and field prediction markets.