Xue-Zhong He, and Nicolas Treich, Prediction market prices under risk aversion and heterogeneous beliefs, Journal of Mathematical Economics, vol. 70, May 2017, pp. 105–114.


In this paper, we examine the properties of prediction market prices when risk averse traders have heterogeneous beliefs in state probabilities. We show that the equilibrium state prices equal the mean beliefs of traders about that state if and only if the traders’ common utility function is logarithmic. We also provide a necessary and sufficient condition ensuring that the state prices are systematically below or above the mean beliefs of traders, thus providing a rational explanation to the favorite-longshot bias in prediction markets.


Prediction market; Heterogeneous beliefs; Risk aversion; Favorite-longshot bias;

Research partnership

Scor Chair (centre sustainable)