The only thing that all four market structures have in common is that firms in all four are trying to maximize profits or minimize losses. And they all do this by producing at the quantity where marginal revenue equals marginal costs.
Other than that, there is nothing that they all have in common.
- There are barriers to entry in monopoly but not in the others.
- Firms in perfect competition sell homogeneous products (and firms in oligopoly can) the rest sell differentiated products.
- There are many firms in monopolistic and perfect competition, only a few in oligopoly and one in monopoly.