In a two-sided asymmetric information market, the role of the accuracy of consumers’ imperfect and private information on the level of fraud, incidence of fraud and trade under price rigidity is examined. Consumers receive a costless but noisy private signal of quality. The product offered in the market can be of two exogenously given qualities and it is common knowledge that the consumer is not willing to pay a high price for a low quality product. A low quality seller chooses to be either honest (by charging the lower market price) or dishonest (by charging the higher price). We show that equilibria involving fraud exist for all parameter values. Furthermore, for some parameter values, we find that -in equilibrium- a higher precision of consumers’ private information leads to higher levels of fraud and incidence of fraud, reducing consumers’ welfare. We provide conditions for the public revelation of consumers’ private information to be a Pareto improvement.