Bilateral monopoly systems have most commonly been used by economists to describe the labor markets of industrialized nations in the 1800s and the early 20th century. Large companies would essentially monopolize all the jobs in a single town and use their power to drive wages to lower levels. Workers, to increase their bargaining power, formed labor unions with the ability to strike, and became an equal force at the bargaining table with regard to wages paid.
As capitalism continued to thrive in the U.S. and elsewhere, more companies were competing for the labor force, and the power of a single company to dictate wages decreased substantially. As such, the percentage of workers that are members of a union has fallen, while most new industries have formed without the need for collective bargaining groups among workers.
In a bilateral monopoly, the one supplier will look to charge a high price, and the lone buyer will want to pay the lowest possible price.