A Free Market Solution to Pirates

Amid all this concern about pirates in the Indian Ocean, Tim Fernholz notes that the Competitive Enterprise Institute has proposed a free-market solution to the problem of pirates:

[T]he United States should consider authorizing private parties to attack pirate ships under little used instruments called "letters of marque and reprisal."

The letters, specifically authorized in the Article 1 section 8 of the U.S. Constitution, allow private parties to attack and seize the property of other parties that have committed violations of international law. Congress has the power to grant the letters. The United States made significant use of them during the Revolutionary War and the War of 1812 and never joined 19th Century treaties in which European nations forswore their use.

But I wonder if issuing these letters will actually lead to a solution. Is there a huge supply of privateers waiting for a government license to attack pirates? I don't know if there's much profit to be had looting Somali pirates off the horn of Africa.