Just by looking at our our Core i7-3770K results above, BioShock Infinite does not appear to be a CPU bound game. Clocking the 3770K from 2.5GHz up to 4.5GHz made for a marginal 4fps difference, so overclocking your Core i7 processor is not going to help improve performance.
The same situation was found when testing the AMD FX-8350 which seemed limited to 65 - 66fps. If you look at frame times, it'd appear however that a faster CPU will result in more fluid gameplay.
Ideally gamers are going to want a Core i5 or FX-8350 processor for optimal performance, though as we noted above BioShock Infinite is not a CPU bound game. Therefore older processors such as the Phenom II X4 will do just fine. Furthermore dual-core options such as the Core i3 and Phenom II X2 will also suffice. The only processors to show a noticeable decline in performance were the Athlon IIs.