I believe if you had two identical BPs running using the same pool cert, it would look something like this:
They would be using the same nonce and stake to calculate leading slots, so they would each try to create blocks at the same time.
They would each have their own transaction pool (which I think could vary slightly depending on which one receives pending tx’s first etc.). So when they are leader, they would each try to create a block - sometimes the blocks would be identical, in which case I suspect it would work just fine (would love more insight here as I’m not sure about this). If the two blocks contain a different amount of transactions they would be different, and it would cause a slot battle. If it was just your two nodes competing and no others, one of them will win and the other block will be discarded. There is no penalty for this so I actually don’t see a downside apart from causing the slot battle. I wonder if having the battle would put you at a disadvantage or if it’s just bad for the network.
I’m definitely interested in the perspective of someone who understands the protocol at a deeper level on this one.