Just adding a bit for completeness.
1. The difficulty level of the map does not affect the joining of monsters.
I don't know. But I have repeatedly observed that at a low difficulty level, monsters are more likely to join on their own than at higher levels.
2. 90% of the players on this forum play at the "queen (or king?)" - "extremely difficult" level.
I'm very happy for 90% of the players, but the AI doesn't get any smarter above "rook." After that, it just reduces the player's resources and increases the computer's resources. In my opinion, it's a pointless challenge. But this is already off-topic.