The city of Yokosuka, Kanagawa Prefecture, home to the U.S. 7th Fleet, has no problem extracting dollars from the hands of American sailors. What it really wants to do is prize greenbacks from the pockets of Japanese customers.

A private-sector estimate puts that amount at more than ¥1 trillion, in bills and loose change left over from trips overseas.

In 2013, the Yokosuka city office began a campaign offering gifts to Japanese tourists who collect stamps at shops in the area after paying for goods in dollars.