I recall reading this novel in the ’90s; my recollection is that the author was better-known for bad fantasy than for SF (but the SF of his that I’d read was better than his fantasy).
The story opened in media res just before a battle was joined; there is a dialogue between the captain of one of the ships and one of his crew. We never see the actual battle; we instead see the conquest of Earth by the aliens - and the conquest of the alien homeworld by Earth.
It is slowly revealed that the two sides contrived a way to both avoid the destruction of actual war, and solve their respective worlds’ respective problems of overpopulation, infrastructure decay, et multae ceterae. We also see that the solution was that the conquering aliens were secretly selecting Earthmen to rule their homeworld, while the humans were selecting aliens to rule Earth.
About halfway through, there is suddenly a third world that must be ‘conquered’ and brought into the network. The plot gets complicated after that.