This study investigates the asymptotic behavior of solutions of the two-region dynamic Dixit-Stiglitz-Krugman model with discrete-time variable. This model comprises the core-periphery model and replicator equations, and suggests that manufacturing workers relocate based on wages as time increases. Previously, Tabata and Eshima demonstrated the existence of solutions for the core-periphery model. Using their result, a sufficient condition is provided for manufacturing workers, which are solutions of the dynamic Dixit-Stiglitz-Krugman model, to realize agglomeration in one region as time increases. In addition, numerical computation is performed to reveal the main results and insights regarding periodic solutions of the dynamic Dixit-Stiglitz-Krugman model.