My theory after the Lighthouse is this...Jacob and MIB are playing a game with peoples lives and the winner gets to leave the island. Jacob is wagering that he can find one worthy candidate meeting some mysterious criteria, among X number of people; and MIB is wagering that all X number of people will be found wanting, and thus die on the island.
We now know that they each have a place to keep score and cross of names at their own leisure. Of all the names written in the cave and the lighthouse, only 6 are not crossed off. So if this is near the end of the game, Jacob, after crossing off names for decades or more, may have a very small pool of candidates to work with. And if MIB can win the game by crossing off the final six names, then he may have nothing on his mind besides orchestrating the death of the last few candidates.