2016/14 LEM Working Paper Series

Far from the Madding Crowd: Collective Wisdom in Prediction Market

Giulio Bottazzi and Daniele Giachini
Prediction Markets, Bet Pricing, Wisdom of Crowds, Market Selection, Heterogeneous Beliefs, Fractional Kelly Rule

  JEL Classifications
C60, D53, G11, G12

We investigate market selection and bet pricing in a simple Arrow secu- rity economy which we show is equivalent to the repeated prediction mar- ket models studied in the literature. We derive the condition for long run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of two fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true prob- abilities. Nor are they always nearer to the truth than the believes of all surviving agents. Moreover, we show that by adapting their beliefs to past prices, agents further decrease the agreement between market prices and true probabilities.
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