Capitalism as a Local Optimizer?

I remember learning in economics that some folks got a Nobel Prize about 50 years ago for a proof that free markets lead to optimal policies. I wonder if anyone has investigated the assumptions in the proof in the sense that I wonder if it's really just a local optimizer (finding the nearest peak) rather than finding the best global solution (the real top of the mountain).

All proofs about the real world, of necessity, rely on assumptions and approximations. Just wondering what they are here.

I also wonder, because it seems to me like capitalism works well but is short-sighted. I'd be curious if this intuitive feel could be worked out mathematically.

Note: I'm not an economics expert, so I don't know what's been researched on this subject before.