The research-intensive and competitive knowledge society is putting HEIs (higher education institutions) under the spotlight. While many HEIs around the world do not proclaim or wish to be research-intensive institutions the majority desire to intensify their research activity because it is seen as a sine qua non of higher education. Accordingly, HEIs are busy making critical strategic choices concerning human resources, the research environment, the teaching-research nexus, organisational and management structure, and funding. Governments are also making choices, using policies and financial instruments to help shape institutional mission, priorities and HE systems. But if governments genuinely desire to widen access to the knowledge society and achieve a greater contribution from higher education to economic and social development more is required. This paper applies Porter's diamond of competitive advantage to illustrate the complex relationship between institutional mission and policy constraints, proposing changes in strategy and policy to unlock potential. There are important lessons for both institutions and government.