In this paper, we discuss how fraud losses impact the price structure chosen by a monopolistic payment platform, if merchants can invest in fraud detection technologies. We show that liability rules bias the structure of the prices charged by the platform to consumers and merchants with respect to a case in which such a responsibility regime is not implemented. If consumers are liable for fraud, the profit-maximizing price structure is neither biased in favor of consumers nor merchants. If consumers are not liable for fraud, the platform lowers the price for merchants to provide them with investment incentives. Under the zero liability rule for consumers, the profit-maximizing allocation of fraud losses maximizes social welfare