We propose an agent-based dynamics which leads an urban system to the standard equilibrium of the Alonso, Muth, Mills (AMM) framework. Starting for instance from a random initialization, agents move and bid for land, performing a kind of local search and finally leading the system to equilibrium rent, density and land use. Agreement with continuous analytical results is only limited by the discreteness of simulations. We then study polycentrism in cities with this tool. Two job centers are introduced, and the economic, social and environmental outcomes of various polycentric spatial structures are presented. We also introduce two-worker households whose partners may work in different job centers. When various two-worker households are mixed, polycentrism is desirable, as long as centers are not moved too far apart from each other. The environmental outcome is also positive, but housing surfaces increase.