## Theoretical investigation of prediction markets with aggregate uncertainty (2004)

Venue: | In Proceedings of the Seventh International Conference on Electronic Commerce Research (ICECR-7 |

Citations: | 4 - 3 self |

### BibTeX

@INPROCEEDINGS{Chen04theoreticalinvestigation,

author = {Yiling Chen and Tracy Mullen and Chao-hsien Chu},

title = {Theoretical investigation of prediction markets with aggregate uncertainty},

booktitle = {In Proceedings of the Seventh International Conference on Electronic Commerce Research (ICECR-7},

year = {2004}

}

### OpenURL

### Abstract

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

### Citations

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(Show Context)
Citation Context ...p models to formally understand how prediction markets work and to suggest methods to improve its performance. Research in this category is very fundamental and important. Dating back to 1976, Aumann =-=[1]-=- presented the formal definition of common knowledge and studied how two people can agree with each other. Aumann proved that if two people have the same priors, and their posteriors for some event ar... |

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Citation Context ...ticipants trade securities whose payoffs depend on outcomes of the presidential election. Analysis of trading data found that prices in these markets predicted the election outcomes better than polls =-=[2, 3, 8, 9]-=-. Some other online game markets include Hollywood Stock Exchange (HSX) 2 , Foresight Exchange (FX) 3 , Formula One Pick Six (F1P6) 4 . HSX trades securities based on future box office proceeds of new... |

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Citation Context ... The process continues until an equilibrium is reached, after which prices and bids do not change from stage to stage. The above trading process is essentially a simplified Shapley-Shubik market game =-=[20]-=-. Feigenbaum et al. [5] use the same trading mechanism in their model, but formulated in a different way. 3.3 Trader strategy We make the assumption that traders will bid their expected payoff of a un... |

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Citation Context ...e common knowledge, then these posteriors must be equal. However, it is very rare that two people can have common knowledge about their posteriors at the very beginning. Geanakoplos and Polemarchakis =-=[11]-=- extended Aumann’s work by demonstrating that if two people with common priors successively announce their posteriors to each other, eventually this leads to a situation of common knowledge where thei... |

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Citation Context ...s a random variable, prediction markets can function as a powerful tool for generating forecast about the event. Such prediction markets have been proved effective in many domains, including politics =-=[7, 8, 9]-=-, entertainment [22], and sports [4, 10]. Implemented properly, prediction markets have the potential to assist businesses, universities, and governments making critical decisions. Currently, predicti... |

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Citation Context ...n function as a powerful tool for generating forecast about the event. Such prediction markets have been proved effective in many domains, including politics [7, 8, 9], entertainment [22], and sports =-=[4, 10]-=-. Implemented properly, prediction markets have the potential to assist businesses, universities, and governments making critical decisions. Currently, prediction markets are in their primitive stage.... |

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Citation Context ...s a random variable, prediction markets can function as a powerful tool for generating forecast about the event. Such prediction markets have been proved effective in many domains, including politics =-=[7, 8, 9]-=-, entertainment [22], and sports [4, 10]. Implemented properly, prediction markets have the potential to assist businesses, universities, and governments making critical decisions. Currently, predicti... |

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Citation Context ...participants can predict Formula One International race car competition results. Prices of securities in these markets were found to give as accurate or more accurate predictions than expert opinions =-=[17, 18]-=-. 3 A model of prediction markets with aggregate uncertainty The model of the prediction market in Feigenbaum et al. [5] does not consider aggregate uncertainty. In their model, each trader possesses ... |

23 |
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Citation Context ...n function as a powerful tool for generating forecast about the event. Such prediction markets have been proved effective in many domains, including politics [7, 8, 9], entertainment [22], and sports =-=[4, 10]-=-. Implemented properly, prediction markets have the potential to assist businesses, universities, and governments making critical decisions. Currently, prediction markets are in their primitive stage.... |

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Citation Context ...information disagree with the expected value of the security at the beginning. By trading in the market, they gradually reach an agreement, which is represented by the market price. Feigenbaum et al. =-=[5]-=- analyzed some computational properties of information market. They modeled an information market, in which there is no aggregate uncertainty. The random variable to be predicted is a function of all ... |

11 |
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(Show Context)
Citation Context ...certainty. Their results demonstrated that market structures are important for information aggregation. Only with an appropriate market structure, can a market aggregate diverse information. Lundholm =-=[13]-=- examined the effect of aggregate uncertainty and found that markets aggregate information less efficiently when there is greater aggregate uncertainty. Forsythe and Lundholm [6] studied the effect of... |

11 |
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(Show Context)
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9 |
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Citation Context ...s a random variable, prediction markets can function as a powerful tool for generating forecast about the event. Such prediction markets have been proved effective in many domains, including politics =-=[7, 8, 9]-=-, entertainment [22], and sports [4, 10]. Implemented properly, prediction markets have the potential to assist businesses, universities, and governments making critical decisions. Currently, predicti... |

2 |
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Citation Context ...participants can predict Formula One International race car competition results. Prices of securities in these markets were found to give as accurate or more accurate predictions than expert opinions =-=[17, 18]-=-. 3 A model of prediction markets with aggregate uncertainty The model of the prediction market in Feigenbaum et al. [5] does not consider aggregate uncertainty. In their model, each trader possesses ... |