Journal article: This paper evaluates the role of competition and input-output market access in shaping the geography of economic activity. In a first step, we develop a multi-region multi-industry economic geography model under Cournot competition, of which we estimate the parameter values from French data. We then turn to simulations to see whether a core-periphery equilibrium exists, even with strategic interactions among firms. We show that the marginal profits and mark-ups of firms are greater in both core and peripheral regions than in between, due to a subtle interplay between competition and market-access forces. Production is mostly monocentric, however, and profits are higher in the core, which should produce further concentration. We finally show that policy-makers face a difficult trade-off: lowering inter-regional trade costs reduces disparities between regions, but increases intra-regional inequality.