Using computational modeling, we design a pair of biomimetic microcapsules that exploit chemical mechanisms to communicate and alter their local environment. As a result, these synthetic objects can undergo autonomous, directed motion. In the simulations, signaling microcapsules release "agonist" particles, while target microcapsules release "antagonist" particles and the permeabilities of both capsule types depend on the local particle concentration in the surrounding solution. Additionally, the released nanoscopic particles can bind to the underlying substrate and thereby create adhesion gradients that propel the microcapsules to move. Hydrodynamic interactions and the feedback mechanism provided by the dissolved particles are both necessary to achieve the cooperative behavior exhibited by these microcapsules. Our model provides a platform for integrating both the spatial and temporal behavior of assemblies of "artificial cells", and allows us to design a rich variety of structures capable of exhibiting complex dynamics. Due to the cell-like attributes of polymeric microcapsules and polymersomes, material systems are available for realizing our predictions.