I prove that competitive market outcomes require computational intractability. If P = NP, firms can efficiently solve the collusion detection problem, identifying deviations from cooperative agreements in complex, noisy markets and thereby making collusion sustainable as an equilibrium. If P != NP, the collusion detection problem is computationally infeasible for markets satisfying a natural instance-hardness condition on their demand structure, rendering punishment threats non-credible and collusion unstable. Combined with Maymin (2011), who proved that market efficiency requires P = NP, this yields a fundamental impossibility: markets can be informationally efficient or competitive, but not both. Artificial intelligence, by expanding firms' computational capabilities, is pushing markets from the competitive regime toward the collusive regime, explaining the empirical emergence of algorithmic collusion without explicit coordination.

翻译：本文证明竞争性市场结果需要计算上的难解性。若 P = NP，企业可高效解决合谋检测问题，在复杂且充满噪声的市场中识别合作协定的偏离行为，从而使合谋作为均衡得以维持。若 P != NP，对于需求结构满足自然实例困难性条件的市场，合谋检测问题在计算上不可行，导致惩罚威胁不可信且合谋不稳定。结合 Maymin（2011）证明市场有效性需要 P = NP 的结论，这揭示了一个根本性的不可能定理：市场可以实现信息有效性或竞争性，但无法同时实现二者。人工智能通过扩展企业的计算能力，正在推动市场从竞争体制转向合谋体制，这解释了算法合谋在无需显式协调的情况下于实证中出现的现象。