New York Mayor Michael Bloomberg is offering $9 million in prizes to U.S. cities through his charitable foundation in a competition for ideas that local governments can use to solve problems. The contest, which Bloomberg Philanthropies calls the Mayors Challenge, starts today when the foundation sends invitations to compete to 1,300 mayors of U.S. cities with more than 30,000 residents. They have until Sept. 14 to enter their submissions, said James Anderson, director of the charity’s government-innovation program. The winner, to be announced next year, will receive $5 million, and four runners-up will each get $1 million. New York City isn’t eligible, Anderson said.