We study the formation of monopolies in a simplified economic model where two brands compete in the market, using an agent based model. Each agent represents a company that uses one of the two available brands and interacts with other companies. The brands continually improve their product in order to compete for market share. In the innovation process companies can decide to change to the other brand if the move is beneficial. There is a cost for the company if it decides to switch to the other brand, and another cost if it stays with its current brand but only upgrades to a new enhanced version of the product. Our simulations show that the system always reaches a state when all companies end using a single brand, which is equivalent to a monopoly. We study the time span needed to reach the single brand final state for different parameters of the model.