Peer-assisted content distribution matches user demand for content with available supply at other peers in the network. Inspired by this supply-and-demand interpretation of the nature of content sharing, we employ price theory to study peer-assisted content distribution. The market-clearing prices are those which align supply and demand, and the system is studied through the characterization of price equilibria. We discuss the efficiency and robustness gains of price-based multilateral exchange, and show that simply maintaining a single price per peer (even across multiple files) suffices to achieve these benefits. Our main contribution is a system design - PACE (Price-Assisted Content Exchange) - that effectively and practically realizes multilateral exchange. Its centerpiece is a marketbased mechanism for exchanging currency for desired content, with a single, decentralized price per peer. Honest users are completely shielded from any notion of prices, budgeting, allocation, or other market issues, yet strategic or malicious clients cannot unduly damage the system's efficient operation. Our design encourages sharing of desirable content and network-friendly resource utilization. Bilateral barter-based systems such as BitTorrent have been attractive in large part because of their simplicity. Our research takes a significant step in understanding the efficiency and robustness gains possible with multilateral exchange.