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BioShock Infinite: Burial at Sea Episode One has a very cool illustration for the cover artwork:
I initially would say its art style is "noir" but when I did a Google Images search for "noir art" it came up with images that had some similar elements, but they were not very similar to the style above:
Is there a name for this kind of illustration's style?
Interesting. Not entirely sure what part of the style you are after, but I am going to take your noir as a hint.
Actually, I think you are pretty close in your search, but I think you need to use "film noir poster". That will give you a lot of stuff like this:
Another search term is "pulp paperback cover" or "pulp fiction". This is the classic name for paperbacks with simple stories, usually detetctive-ish stuff (pulp refers to wood pulp, the cheap material for producing paperbacks.Hence, pulp fiction). Here is what you might find:
Clearly, your image is a modern version of this style; it is softer, more digital in the lines. But this might get you started.
I could not resist, you might like this site, with pulp-noir covers Here is an example from that site, pulp-noir paintings:
