11 nations have 2 athletes
Only about half the countries on Earth have any athletes at all in the 2014 Olympics, so it's a hundred-way tie for fewest.
There are 11 countries with only 2 athletes
In checking the teams from each country, I found that Nauru has only one athlete participating in the Beijing Olympics. Brunei and Bhutan each have two athletes. There may be other countries with only 1-2 athletes total at the summer Olympic games.
Many countries have 5 or less athletes and it is more than a 10 way tie for those with only 2
More than 10 countries had only 2 athletes
The Caribbean island of Dominica has only two athletes competing in Beijing at the 2008 Olympics. It is the smallest team.
Iran have not provided any athletes this year
Antarctica Well Sealand has one of the fewest people living, but it's not noticed as a country.