In a market where consumers choose between payment options and firms compete with products and prices, we show that payment data drives the formation of a market monopoly. A data-sharing policy can successfully restore and maintain a competitive market, but often at the expense of both efficiency and consumer welfare. The introduction of a low-cost anonymous means of electronic payment, or digital cash, preserves the market structure and improves consumers' welfare by enabling them to monetize their private information. We discuss the potential role of central banks in providing digital cash.