A bilateral monopoly is when there is one buyer and one seller.
When the first IBM PC was introduced, there was one buyer for Microsoft’s operating system (DOS) and one seller. However, IBM allowed other companies to make “clones,” with the result that the hardware became a commodity and the software became worth a fortune.
We rarely observe bilateral monopolies between two firms, because each firm has such a strong incentive to try to create competition on the other side of the bilateral monopoly. Thus, I would argue that bilateral monopoly is more likely to wind up within a firm than across two firms.
Specific human capital, meaning skills that are valuable only in the context of a particular industry or a particular organization, gives rise to bilateral monopoly. An employee who is familiar with the procedures, culture, and systems that are peculiar to one firm is more valuable to the firm than another employee. For the employee, the firm is now a better fit than some other firm.
In the economy as a whole, specialization tends to produce a lot of specific human capital. Thus, many economic relationships have to take bilateral monopoly into account. You can think of these sorts of bilateral monopolies as repeated games, in which cooperating means sharing the rents from specific human capital, and defecting means either trying to appropriate all of the rents or ending the relationship.
Typical contract features that try to deal with these repeated games include increases in pay and benefits tied to length of service, including pension vesting or additional weeks of vacation. Some firms offer training or tuition reimbursement with a requirement that the worker continue with the firm for a period of time afterward.
I think that most of these sorts of contractual features could be reproduced across the boundaries of firms. That is, if I want you to invest in human capital specific to my firm, I can design a contract that induces you to remain in a long-term relationship.
However, there is another type of inducement that is almost inherently within the firm. That is the inducement provided by promotion from within. If you know that internal candidates have an advantage when a high-level position opens up, that gives you an incentive to invest in specific human capital within that firm.
In fact, I believe it is the case that organizations that promote almost entirely from within have very loyal middle managers. The cost is that such organizations can be culturally rigid and stagnant. Conversely, firms that frequently fill high-level positions from outside and/or engage in mergers and acquisitions can be more flexible and dynamic, but at a cost of low morale and high turnover at lower levels of management.