“There’s this ‘Alice in Wonderland’ quality to the question of, what is the public interest here and who’s protecting it?” said Mr. Brodsky, who conducted a hearing on the issue of public financing of sports stadiums this summer. “We can’t find the money for the M.T.A., or schools, or hospitals, and these folks are used to the perks and good things of life, and expect them.”

The city maintains it was simply trying to obtain a luxury suite comparable to that given to other cities involved in stadium or arena projects. But the message traffic, which dates to January 2006, raises questions, too, about how sincere city officials were when they recently stated publicly that the box could be used to reward outstanding city workers, rather than mainly for the mayor, dignitaries and aides. The notion of inviting city workers as guests is not mentioned in the e-mail messages until Aug. 7, 2008, and only then in response to an inquiry from a reporter.

The city’s push for the perks has been known, at least broadly speaking, since Mr. Brodsky began raising questions earlier this year about the stadium deals for the Yankees and Mets, from whom the city also secured a luxury box. But the e-mail messages offer a revealing snapshot of the behavior and marching orders of the people involved in the deal for the construction of the billion-dollar Yankee Stadium.

It is hard to determine the precise value of what the city gave the Yankees as part of the exchange. The public parking, though perhaps a convenience to those who drive to the stadium, was to be run by a parking garage operator, not the city, before it was turned over to the Yankees for team use. The billboards would most likely generate about $750,000 annually, given their location. The Yankees are expected to charge $600,000 to $850,000 a year for stadium luxury suites, according to reports.

The project required permission from the Internal Revenue Service because of the team’s desire to use tax-exempt bonds to finance construction. In one heated exchange, city lawyers threatened they would not make the request to the I.R.S. for the use of the tax-exempt financing unless the Yankees would consider providing the luxury suite.