Do all firms in all market structures have anything in common?

I think not.

They all consist of buyers and sellers.

In Principals of Microeconomics courses, economists make several general economic assumptions (perhaps incorrectly I might add) about firms and the behavior of firms. For example, we generally assume that:
1) All firms are profit maximizers.
2) All firms make rational choices.
3) Consumers make rational choices.
4) The marginal product of inputs is almost always decreasing.

While firms in different market structures may have some differences, there are a few common characteristics that can be found across all firms:

1) Production: All firms engage in some form of production, whether it is producing goods or providing services.

2) Exchange: Firms interact in markets by exchanging their products with consumers or other firms.

3) Cost considerations: Firms need to consider the costs associated with production, such as labor, raw materials, and overhead expenses.

4) Profit orientation: While not all firms are purely profit maximizers, they are generally motivated by the desire to generate income and achieve financial stability.

5) Organizational structure: Firms typically have some form of organizational structure, which includes having a management team and employees.

It is important to note that these commonalities do not imply that all firms are identical or behave in the same way. The behavior and characteristics of firms can vary significantly depending on the market structure they operate in, such as perfect competition, monopolistic competition, oligopoly, or monopoly.