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19
Computation in a Distributed Information Market
, 2003
"... According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information dis ..."
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Cited by 21 (4 self)
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According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information distributed among traders is revealed stepby step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as a weighted threshold function of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.
Information Aggregation in Dynamic Markets with Strategic Traders,” Working Paper
, 2009
"... This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as ..."
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Cited by 21 (0 self)
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This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as time approaches the end of the interval, the market price of a “separable” security converges in probability to its expected value conditional on the traders ’ pooled information. If the security is “nonseparable, ” then there exists a common prior over the states of the world and an equilibrium such that information does not get aggregated. The class of separable securities includes, among others, ArrowDebreu securities, whose value is one in one state of the world and zero in all others, and “additive ” securities, whose value can be interpreted as the sum of traders ’ signals.
Disagreement is Unpredictable
 Economics Letters
, 2002
"... Given common priors, no agent can publicly estimate a nonzero sign for the difference between his estimate and another agent’s future estimate. Thus rational agents cannot publicly anticipate the direction in which other agents will disagree with them. ..."
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Cited by 7 (3 self)
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Given common priors, no agent can publicly estimate a nonzero sign for the difference between his estimate and another agent’s future estimate. Thus rational agents cannot publicly anticipate the direction in which other agents will disagree with them.
Theoretical investigation of prediction markets with aggregate uncertainty
 In Proceedings of the Seventh International Conference on Electronic Commerce Research (ICECR7
, 2004
"... Much evidence supports that financial markets have the ability to aggregate information. When tied to a random variable, a financial market can forecast the value of the random variable. It then becomes a prediction market. We establish a model of prediction markets with aggregate uncertainty, and t ..."
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Cited by 4 (3 self)
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Much evidence supports that financial markets have the ability to aggregate information. When tied to a random variable, a financial market can forecast the value of the random variable. It then becomes a prediction market. We establish a model of prediction markets with aggregate uncertainty, and theoretically characterize some fundamental properties of prediction markets. Specifically, we have shown that a prediction market is guaranteed to converge to an equilibrium, where traders have consensus on the forecast. The best possible prediction a prediction market can make is the direct communication equilibrium. However, prediction markets do not always converge to it. We have proved that a sufficient condition for the convergence to the direct communication equilibrium under our model is that the private information of each trader, conditioned on the state of the world, is identically and independently distributed. Furthermore, if this condition is satisfied, the prediction market converges in at most two rounds. 1
An InDepth Analysis of Information Markets with Aggregate Uncertainty
 ELECTRONIC COMMERCE RESEARCH
, 2006
"... The novel idea of setting up Internetbased virtual markets, information markets, to aggregate dispersed information and predict outcomes of uncertain future events has empirically found its way into many domains. But the theoretical examination of information markets has lagged relative to their ..."
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Cited by 4 (1 self)
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The novel idea of setting up Internetbased virtual markets, information markets, to aggregate dispersed information and predict outcomes of uncertain future events has empirically found its way into many domains. But the theoretical examination of information markets has lagged relative to their implementation and use. This paper proposes a simple theoretical model of information markets to understand their information dynamics. We investigate and provide initial answers to a series of research questions that are important to understanding how information markets work, which are: (1) Does an information market converge to a consensus equilibrium? (2) If yes, how fast is the convergence process? (3) What is the best possible equilibrium of an information market? and (4) Is an information market guaranteed to converge to the best possible equilibrium?
Consensus By Identifying Extremists
"... Abstract. Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies “consensus”, i.e., common knowledge of common expectations. This “extremist ” statistic induces consensus when repeatedly announ ..."
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Cited by 4 (2 self)
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Abstract. Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies “consensus”, i.e., common knowledge of common expectations. This “extremist ” statistic induces consensus when repeatedly announced, and yet, with n agents, requires at most log 2 n bits to broadcast. Key words: consensus, common knowledge, information pooling, Bayesian learning 1.
For Savvy Bayesian Wannabes, Disagreements Are Not About Information
 California Institute of Technology
, 1997
"... Consider two agents who want to be Bayesians with a common prior, but who cannot due to computational limitations. If these agents agree that their estimates are consistent with certain easytocompute consistency constraints, then they can agree to disagree about any random variable only if they al ..."
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Cited by 3 (2 self)
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Consider two agents who want to be Bayesians with a common prior, but who cannot due to computational limitations. If these agents agree that their estimates are consistent with certain easytocompute consistency constraints, then they can agree to disagree about any random variable only if they also agree to disagree, to a similar degree and in a stronger sense, about an average error. Yet average error is a stateindependent random variable, and one agent’s estimate of it is also agreed to be stateindependent. This suggests that disagreements are not fundamentally due to differing information about the state of the world. JEL: D82
Designing informative securities
 In UAI
, 2012
"... We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders’ private signals. We consider the design of markets that are always informativ ..."
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Cited by 1 (1 self)
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We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders’ private signals. We consider the design of markets that are always informative, markets that are informative for a particular signal structure of the participants, and informative markets constructed from a restricted selection of securities. We find that to achieve informativeness, it can be necessary to allow participants to express information that may not be directly of interest to the market organizer, and that understanding the participants’ signal structure is important for designing informative prediction markets. 1