Markets are competitive if and only if P = NP
The paper proves that markets are competitive (no market power) if and only if P = NP, establishing a formal equivalence between a fundamental economic condition and a central problem in computational complexity theory.
Background
This paper claims to formally prove that P = NP — one of the hardest open problems in computer science — using an unexpected argument from economics. P vs. NP asks whether every problem whose answer can be checked quickly can also be solved quickly. It is widely believed that P ≠ NP, and a proof either way would be a landmark result. The paper links this to market competition: roughly, it argues that if markets are perfectly competitive (a standard economic ideal), then P = NP must hold. Because the author is not a known complexity theorist and the claim is extraordinary, the paper is being met with intense skepticism and scrutiny. A correct proof would upend cryptography, optimization, and AI, but most experts expect a flaw.