HTTP adaptive streaming (HAS) has become the universal technology for video streaming over the Internet. Many HAS system designs aim at sharing the network bandwidth in a rate-fair manner. However, rate fairness is in general not equivalent to quality fairness as different video sequences might have different characteristics and resource requirements. In this work, we focus on this limitation and propose a novel controller for HAS clients that is able to reach quality fairness while preserving the main characteristics of HAS systems and with a limited support from the network devices. In particular, we adopt a price-based mechanism in order to build a controller that maximizes the aggregate video quality for a set of HAS clients that share a common bottleneck. When network resources are scarce, the clients with simple video sequences reduce the requested bitrate in favor of users that subscribe to more complex video sequences, leading to a more efficient network usage. The proposed controller has been implemented in a network simulator, and the simulation results demonstrate its ability to share the available bandwidth among the HAS users in a quality-fair manner.