2K games confirmed last year that Cloud Chamber would be taking over the BioShock franchise with a brand new entry in the series. As part of this process, the studio has listed several job positions on its website, some of which have given us a few hints about what the fourth entry in the series might entail.
The suggestion seems to be that the game will be open world rather than the linear affair of previous games, and it'll have both primary and side-quests, both of which scream a more RPG style of gameplay to me. According to the job description for "senior writer," Cloud Chamber is looking for "someone who can weave impactful, character-driven stories in an open-world setting," before going to mention the candidate would be responsible for coming up with "primary and secondary mission content with design."
It seems the game will continue to BioShock tradition of using Unreal Engine, though, with the job listings suggesting UE4 experience is "strongly desired." There's also a lot of mentions within the ads to working on a "living" world, suggesting that the game will indeed be more of an open-ended affair with random encounters and multiple choices. Indeed, one ad, for senior world designer, talks about the successful candidate "design[ing] and create[ing] systemic world moments, as well as bespoke quests, that breathe life into the game."
There's even a reference to an "AI urban crowd system," that will "push the envelope." All of this tells me that this game is very unlikely to take part in Rapture, the setting of the first two BioShock games, and the setting of BioShock Infinite, Columbia, while more likely, seems like a narrative dead-end. In any case, it seems like an exciting and fresh direction for the BioShock franchise, and it'll be interesting to see just where all of this is going.