You can click on states for details; for instance, in Illinois, 69% are insured by the top two companies, Blue Cross Blue Shield (47%) and WellPoint (22%). Says CAP:
Today many Americans have few choices when it comes to health insurance. This is because many insurance markets are dominated by only a handful of firms, even though there are over 1,000 private health insurance carriers in the United States. This concentration limits employers’ and families’ health insurance options as well as the care they receive.Fortunately, though, health insurance companies are entirely benign institutions that seek to promote the common good, and would never think of seeking to profit exorbitantly off of the health needs and suffering of the people who support their businesses.
In many states small insurers compete against one another in the individual market to insure only low-risk, healthy individuals. They refuse to insure Americans with pre-existing conditions [ed.: like me!] such as high blood pressure, asthma, cancer, or diabetes and those who have ever taken certain prescription drugs—and they create barriers to needed care for those who are insured.
The map shows that in many states insurance markets are dominated by only one or two insurance carriers. In at least 21 states, one carrier controls more than half the market. More than half of the market is controlled by two carriers in at least 39 states. In 2007, a survey conducted by the American Medical Association found that in more than 95 percent of insurance markets, a single commercial carrier controlled at least 30 percent of the insurance market.
Where markets are dominated by only a few firms, health insurers revenues are growing faster than health inflation as insurers maximize rates they charge employers and families and create barriers to care.Listen, free marketeers: the insight that competition breeds innovation is wonderful - but it is not the end of economic analysis. It seems ridiculous to have to point this out, but it's not the case that efficiency and quality will be maximized for every single conceivable good by leaving it to the whims of the marketplace. National defense is not like that, education is not like that, and in a sane world - or in Europe - it would be manifestly obvious that health care is not like that.