What is Complementary Monopoly?

Legal Definition
In a complementary monopoly, consent must be obtained from more than one agent in order to obtain the good. This effect was originally observed in Cournot. The leads to a reduction in surplus generated relative to an outright monopoly, if the two agents do not cooperate.

This can be seen in private toll roads where more than one operator controls a different section of the road. The solution is for one agent to purchase all sections of the road.

Complementary goods are a less extreme form of this effect. In this case, one good is still of value even if the other good is not obtained.
-- Wikipedia