For a simple algorithm to track relationships, you might use something like: $$R = P \times I + C$$ Where:

This formula could be a basic model for how relationships evolve in the game.

In this model, the protagonist is already married to the primary love interest when the story begins. Additional harem members exist, but they are explicitly framed as secondary, unrequited, or comic relief.

The rise of this genre correlates with three major cultural shifts.

The poster child for the "meta-fix." Catarina Claes is so oblivious that she accidentally creates a harem, but the narrative is "fixed" because she is not trying to conquer anyone. By the second season, the harem members realize they all love her and, crucially, begin cooperating as a support network rather than rivals. The harem is "fixed" into a friend group.