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.