Although bacteria are unicellular organisms, they have the ability to act in concert by synthesizing and detecting small diffusing autoinducer molecules. The phenomenon, known as quorum sensing, has mainly been proposed to serve as a means for cell-density measurement. Here, we use a cell-based model of growing bacterial microcolonies to investigate a quorum-sensing mechanism at a single cell level. We show that the model indeed predicts a density-dependent behavior, highly dependent on local cell-clustering and the geometry of the space where the colony is evolving. We analyze the molecular network with two positive feedback loops to find the multistability regions and show how the quorum-sensing mechanism depends on different model parameters. Specifically, we show that the switching capability of the network leads to more constraints on parameters in a natural environment where the bacteria themselves produce autoinducer than compared to situations where autoinducer is introduced externally. The cell-based model also allows us to investigate mixed populations, where non-producing cheater cells are shown to have a fitness advantage, but still cannot completely outcompete producer cells. Simulations, therefore, are able to predict the relative fitness of cheater cells from experiments and can also display and account for the paradoxical phenomenon seen in experiments; even though the cheater cells have a fitness advantage in each of the investigated groups, the overall effect is an increase in the fraction of producer cells. The cell-based type of model presented here together with high-resolution experiments will play an integral role in a more explicit and precise comparison of models and experiments, addressing quorum sensing at a cellular resolution.