Concurrent decision-making networks represent decision systems where the utility of a component (node) becomes dominant by repressing other nodes. These networks are commonly used in modeling competitive interactions in the computational, biological, and social sciences. Most of the existing studies about concurrent decision-making focus on equilibrium convergence of the utilities. However, there are many cases where oscillations can arise. Here, we consider concurrent decision-making networks that follow a two-dimensional lattice topology where one node is a source of oscillations. We investigate the propagation of oscillations in the network, specifically by determining the conditions that will drive the other nodes to also exhibit oscillating utilities and the conditions that will allow the oscillations to dampen or persist. Our simulations show that the two-dimensional lattice structure of a concurrent decision-making network is enough to diminish the amplitude of propagating oscillations. Our results are important in the study of robustness of complex networks against fluctuations and can be starting points in the study of oscillation propagation in other types of interaction networks.