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In this paper, we examine a nonlinear concurrent decision-making model (CDM) of interaction networks that involve more than two antagonistic components (e.g., proteins, species, communities, mental choices). The model assumes sigmoid kinetics where every component stimulates itself but represses all others. We are able to prove general dynamical properties of the CDM (e.g., location and stability of steady states) for any dimension of the state space even if the reciprocal antagonism between two components is asymmetric. There are cases where asymmetric interaction generates oscillatory behavior. Some parameters can serve as biological regulators for inducing steady state switching by leading a temporal state to escape an undesired equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state with the desired component having the dominant value. We further show that perpetually adding an external stimulus can shutdown multi-stability of the system that increases the robustness of the system against stochastic noise.