Imagine sharing a room with 80 competitors for a $5 million grand prize. Now, imagine that room as Bloomberg Philanthropy’s plush headquarters in Manhattan, with the likes Arianna Huffington, Charlie Rose, Michael Bloomberg and Google CEO Chairman Eric Schmidt milling about, participating in special events.

Under these circumstances, it might not be your first instinct to help the others refine their proposals and give them a better chance of winning the grand prize. Yet that’s what the Mayors Challenge, a Bloomberg-issued grant program seeking innovative local solutions to urban problems, has accomplished.

After a total of 300-plus submissions were whittled down to 20, representatives from each finalist city gathered in New York earlier this month to undergo a two-day boot camp of sorts. Dubbed the “Ideas Camp,” the goal was to help refine their proposals before making final submissions at the end of the year. This manifested in group workshops, master classes, a speaker series and peer-to-peer feedback sessions.

The purpose of the Ideas Camp, according to Bloomberg Philanthropies’ James Anderson, was to stress test assumptions and hypotheses via peer comments and expert assistance — a type of competitive collaboration based on a model from Nesta, a UK-based investment and grant making organization. Mayor Madeline Rogero of Knoxville, Tenn., one of the few actual mayors in attendance, noted that she couldn’t “think of a time in my 30-some years of doing this work where a foundation has brought us in as we were competing with one another to further develop our ideas.”

Carlee Alm-LaBar, a representative of Lafayette, La., said that not only was her own city’s idea strengthened, especially through the prototyping classes, but that she returned home inspired to promote other cities’ ideas. According to Luke Butler of the Philadelphia team, “it was a really interesting process of forcing cities to look at their proposals from different perspectives, break them down and then build them into better ideas — a kind of competitive creative destruction process.”

Jamie Emmons, chief of staff for Mayor Jim Gray of Lexington, Ky., said, “regardless of who wins the grant, I think [Bloomberg Philanthropies] accomplished their goal. It certainly made us think differently, and I’m sure the other 19 cities have their eyes wide open about innovation in government now.”

The consensus among the city representatives interviewed was that competitive collaboration was key to success at the Ideas Camp. From the beginning, when representatives had to make their pitch one-on-one to other cities as an ice-breaker, to the end of the day, when they exchanged contact info to follow up with future suggestions, the collaborative nature of the grant program was apparent. According to Butler, “it reinforced the reality that cities all across America are dealing with similar challenges and we should share ideas and work together to help each other solve them.” In fact, many left the process wondering how they could apply an Ideas Camp-like experience to their own city programs (though all agreed that funding likely doesn’t exist to pull it off to the level that Bloomberg has).

The cities left New York with a handful of new contacts, a personal coach to help continue the process and numerous tools to help further strengthen their ideas. Though only a few cities will ultimately receive funding, each one now has a complete proposal addressing a major city problem, and most plan on instituting their plan with or without the funding program from Bloomberg.