This study examines how competitive and cooperative relationships within R&D consortia influence member firms’ innovation output. We propose a U-shaped relationship between the presence of market competitors for a member firm and the firm's joint R&D output with other consortium members, and examine how the relationship is mediated by interactions with other members at the firm level and moderated by collaborative efforts at the consortium level. Using a unique sample of 320 firms from 52 R&D consortia in China, we find support for our predictions. This multi-level study extends our understanding of competition and cooperation in multi-party networks and provides insights for creating a balance between the two forces that is conducive to innovation.