Modelling a market with differentiated products

In microeconomics, the simplest and most basic model is the supply-demand model with price and quantity of the two axes. In this modern time, what determines the sales of goods and services is far more than the price itself, especially when people are getting wealthier and most of these goods and services are getting more affordable. Moreover, firms are more willing to use non-price competition strategies, especially product differentiation. When products are differentiated, we choose products based on our own preferences besides their prices. Therefore, the supply-demand model can be less effective. If we only model one differentiated product, and exclude all other similar products, then we model a monopoly market. However, it is not a monopoly market indeed. However, if we apply a game theory, and firms are the players in the game, there is a general preference function of the market that represent different market shares when the products different prices and different functions, then firms will choose the market shares by choosing the price targets and the qualities of their productions according to their different costs of production.