A new paper proves markets stay competitive only if P≠NP. The thread's rebuttal: we watch cartels fix prices all the time

The theorem: competition needs problems too hard to solve

Philip Maymin's *Markets are competitive if and only if P ≠ NP* turns antitrust into complexity theory. The chain: sustaining a cartel requires credibly punishing defectors; punishing defectors requires detecting them; and detecting a deviation from a collusive agreement, under a natural hardness assumption on demand structure, is computationally hard. So if P = NP, firms could detect cheating efficiently, threats stay credible, and collusion is stable. If P ≠ NP, detection is infeasible, threats collapse, and markets stay competitive by default.

Stacked on his earlier result — markets are *efficient* iff P = NP — it produces a genuine impossibility: an informationally efficient market and a competitive one are mutually exclusive. He then argues AI expands firms' computational reach toward the collusive regime, and floats "computational antitrust": treating hardness itself as a market-design safeguard.

"And yet we've clearly observed stable price fixing cartels"

The thread admired the construction and rejected the empirics. The killer objection was a fact:

"the collusion detection problem is computationally infeasible … rendering punishment threats non-credible and collusion unstable. And yet we've clearly observed stable price fixing cartels… When theory is contradicted by the evidence, it would be wise to consider the theory is flawed." — a commenter pointing at real observed cartels

The complexity-theory crowd attacked the load-bearing word "infeasible":

"This offers little because while P != NP, in most practical cases it doesn't matter. NP problems gets solved with heuristics every day." — a commenter on the gap between worst-case and practical hardness

Another placed the result in context — interesting, but not surprising, since NP-completeness is the norm, not the exception once a system is complex enough. And the policy leap drew a philosophy foul:

"establishing what regulators ought to do requires far more rationale than mere math. It requires a bridge from 'is' to 'ought.' It reminds me of Hume's warning about this kind of non-sequitur…" — a commenter flagging the is/ought jump in 'computational antitrust'

The takeaway the thread hands an economist: the biconditional is a lovely worst-case statement, but real markets run on average cases, and cartels — like the traveling salesman — get solved well enough in practice to make the theorem's neat dichotomy leak everywhere it touches reality.