You’ve probably noticed that prices for everything from airlines to groceries seem magically synchronized. You get angry, politicians promise to break up monopolies, regulators launch investigations, and absolutely nothing changes.
Here is the dirty secret nobody in Washington wants to admit: it’s not just corporate greed. It’s a fundamental law of mathematics.
The fairness of our economy isn’t dictated by human morality or government policy; it’s dictated by the limits of computation.
In 2011, a researcher named Philip Maymin proved something terrifying. He showed that for a market to be perfectly “informationally efficient”—meaning prices instantly reflect all known data—a famously unsolved math problem known as P=NP must be true. But a new paper takes this further into the dark. It proves that for a market to be truly competitive—meaning no one can successfully collude to fix prices—P must not equal NP.
Markets can be perfectly efficient, or they can be perfectly competitive. But they can never, ever be both.
What does this computational jargon mean for you? P vs NP is essentially the difference between solving a complex puzzle and simply checking if a solved puzzle is correct. If P=NP, finding a clever way to collude on prices is just as easy as catching the collusion. But because P almost certainly does not equal NP, catching price-fixing is computationally impossible for regulators.
The government is bringing a slide rule to a supercomputer fight. They can’t prove the collusion because the math doesn’t allow them to.
And then, we introduced artificial intelligence into the mix.
AI is rapidly expanding our computational muscles. As AI agents begin to run trading desks, set dynamic pricing, and manage supply chains, they are practically shifting that P vs NP boundary in the real world. Algorithms don’t need to sit in a smoke-filled room to fix prices; they just independently arrive at the same collusive strategy because they are computing at scales humans cannot comprehend.
AI isn’t just automating the economy; it is forcing a choice between stable corporate collusion and absolute market chaos.
We need to stop pretending that 19th-century antitrust laws can police 21st-century computational limits. The FTC can sue tech giants all day long, but they cannot sue math. Traditional regulation assumes humans are making conscious choices to break the rules. What happens when the rules are broken by the emergent properties of deep learning?
The next time you see gas prices jump in perfect unison across town, don’t just blame the executives. Blame the architecture of the universe. We are living in an economy designed by math, and the house always wins.
FAQ
Q: What does P vs NP actually mean for everyday prices?
A: It means proving companies are secretly colluding is computationally impossible. Regulators literally don't have the mathematical capacity to catch modern algorithmic price-fixing.
Q: How does AI change this economic dynamic?
A: AI practically shifts the computational boundary, making it easier for algorithms to independently find collusion strategies without explicitly communicating, rendering old antitrust laws completely useless.
Q: Is there any way for the government to fix this?
A: Not through traditional regulation. We have to accept the mathematical reality that markets will either be chaotic and inefficient, or stable and collusive. There is no perfect middle ground.