We present a linear agent based model on brand competition. Each agent
belongs to one of the two brands and interacts with its nearest neighbors. In
the process the agent can decide to change to the other brand if the move is
beneficial. The numerical simulations show that the systems always condenses
into a state when all agents belong to a single brand. We study the
condensation times for different parameters of the model and the influence of
different mechanisms to avoid condensation, like anti monopoly rules and brand
fidelity.Comment: Accepted in: International Journal of Modern Physics