Prediction markets are specific financial markets designed to produce forecasts of future events, such as political election outcomes or economic policy decisions. Empirical studies have exhibited over the years the significant accuracy of these anticipations, which tends to give credit to the efficicent market hypothesis advocated by the literature. However the latter relies theoretically on rational behaviors, in sharp contrast with traders' actions observed on most prediction markets. Indeed, an important fraction of participants are subject to several judgement bias. Based on Ottaviani and Sorensen's (2010) approach, we develop a framework that allows to introduce these biased traders and to study the consequences on the equilibrium properties.