March 18 (Bloomberg) — A snapshot of Obamacare enrollment in seven states suggests the law hasn't significantly increased competition in health insurance markets, the Kaiser Family Foundation reported.

In California, for example, four big insurers have largely carved up the state's market. The divide is more equitable than before the Patient Protection and Affordable Care Act as California's insurance market is now "moderately concentrated" instead of "highly concentrated," according to a measure of market share called the Herfindahl-Hirschman Index, said researchers at Kaiser, a Menlo Park, California-based nonprofit that focuses on health care.

"There are some examples of smaller or newer plans being able to get a sizable piece of the market in the exchanges, but by and large a lot of the players in the exchanges that are the biggest were the biggest before as well," Cynthia Cox, a senior analyst at Kaiser, said in a phone interview.