The mayor of Duluth, Minn., threw himself into the ice-ringed waters of Lake Superior. The mayor of Sarasota, Fla., immersed himself in a tank filled with bonnethead sharks, simply to one-up him. The mayor of Wilmington, N.C., said that he would even jump out of an airplane — with a parachute, of course.

They are vying not so much for voters’ attention as Google’s attention. Google has said it plans to build — at no charge — an ultra-high-speed broadband network for 50,000 to 500,000 customers in one or more American cities.

And that offer has become catnip for city leaders, civic boosters and economic development types across the nation. America lags most other industrialized countries in high-speed Internet access. Even though the Obama administration last week unveiled a plan that would move the country forward, it will probably be snared in Congressional infighting for some time.

Image Don Ness, the mayor of Duluth, center, jumped into icy Lake Superior for a bigger catch than Richard Brown's, at left. Credit... Clint Austin/Duluth News Tribune

Meantime, Google’s offer of a network with speeds of one gigabit per second, or 100 times faster than many of today’s high-speed connections, could be a great selling point for a recession-plagued town. With hundreds of cities expected to apply before the deadline on Friday, city officials are using stunts in the hope their bids will stand out. And for those who put together a winning proposal, success may well be a swift path to re-election.