You are right that the Swiss government is composed of 7 members. But you are wrong about the collective head. The Swiss parliament elects every year one of the government members to the presidency. So Switzerland has a president, even if his/her role is purely representative and the his/her presidency lasts just for that year.
Key U.S. House Democrat cites troublesome issues in Iran nuclear deal (Reuters)
from the article: Czech ‘Joe Lieberman’ could be the EU’s first Jewish president