Markets are competitive if and only if P = NP

Philip Maymin proves that competitive markets require computational intractability (P ≠ NP), as firms with sufficient computing power can solve collusion detection problems and sustain cartels. Combined with prior work showing market efficiency requires P = NP, this creates a fundamental tradeoff: markets cannot be both informationally efficient and competitive. Advancing artificial intelligence is expanding firms' computational capabilities, thereby pushing markets toward collusion and explaining algorithmic collusion in practice.