As the first open enrollment period for Obamacare closes, President Obama is declaring victory for hitting 6million sign-ups in the new health care exchanges. But what’s missing amid the cheering is the hard fact that not all enrollments are created equal. This isn’t just a matter of whether healthier people sign up for any plan at all. For the exchanges to offer real choice to consumers, the healthy—including the “young invincibles” we’ve heard so much about—have to enroll in the more generous plans available. If they don’t do that in large numbers, as appears to be likely, the dire predictions about the system as a whole could come true when it comes to the premium plans. Recent economic research suggests that the Affordable Care Act may well fall prey to this trap. The premium options could disappear, forcing every participant in the exchanges into a bare-bones plan.

The good news is that research we have just completed suggests a solution to this problem that upends the conventional wisdom on both left and right that more competition is better for insurance markets. Our proposal is simple if surprising: Regulators should limit competition by only allowing only the biggest health insurance companies to participate in the exchanges. In short, we need an Obamacare oligopoly.

The problem is that free competition can easily ruin insurance markets. To see why, imagine there were just two plans: bronze and platinum, the lowest- and highest-quality plans available under the ACA. If almost all healthy people opt for bronze, as preliminary numbers suggest is likely, leaving the older and sicker in platinum, the cost of platinum plans will become prohibitive because the health care costs of the sick are so high. This would drive the platinum plans out of the market, leaving only .bronze. That’s better than nothing, but it is a far cry from the aims of the law’s drafters, to give every America access to good health insurance and fair prices.

Read more at Slate.com