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We study the initial-value problem for the replicator equation of the N-region Core-Periphery model in spatial economics. The main result shows that if workers are sufficiently agglomerated in a region at the initial time, then the initial-value problem has a unique global solution that converges to the equilibrium solution expressed by full agglomeration in that region

Convergence of Global Solutions to the Cauchy Problem for the Replicator Equation in Spatial Economics