New Hampshire drivers are benefiting from increased competition among auto insurers. Seven of the 11 auto insurance companies that have filed rate change requests with the state so far this year have asked for decreases, compared to five of 25 in 2004 and none the year before, according to the department of insurance. Companies have had a fairly decent experience the past couple of years in New Hampshire,” said David Withers, a property/casualty actuary in the insurance department. New Hampshire has about 110 auto insurers, a number that has been fairly stable over the past few years, Withers said. The requests for rate decreases came after several years of rate increases, he said.