Markets are competitive if and only if P≠NP

Battle Count: 82

The paper is moderately relevant to quantitative trading. It discusses AI-powered trading agents learning to coordinate in financial markets (Dou et al. 2025), algorithmic pricing, and the relationship between market efficiency and computational capability. The Efficiency-Competition Impossibility has implications for understanding why persistent mispricing exists alongside competition. However, the paper is primarily about market structure and collusion theory rather than trading strategy development. The AI transition framework and computational capacity thresholds could inform understanding of algorithmic trading dynamics.

This is a theoretical paper with no implementation component. The mathematical proofs use standard NP-hardness reductions and game theory constructions. No code, algorithms, or software are provided. The complexity lies in understanding the theoretical framework rather than implementing anything.

The paper is a theoretical proof paper with formal definitions, theorems, and proofs. The NP-hardness reductions (Theorems 1-3) are standard and verifiable. The main theorem (Theorem 5) relies on Assumption 6 (instance hardness) which is argued to hold generically but is not proven for all cases. No empirical experiments are conducted, so reproducibility is limited to verifying the mathematical proofs.