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WASHINGTON — Pssst: America’s colleges and universities know a way to stop, and even reverse, their big annual increases in tuition. They have a plan up their sleeves to make sure all of their financial aid goes to the students who need it the most.

All they want is for you to trust them. And an exemption from federal antitrust laws that ban consultation about prices and discounts among competitors in any industry.

So far only the subject of quiet talks with congressional committees that oversee legal policy and higher education, the idea of exempting anyone from antitrust law is hugely controversial, even to fix a problem as daunting as high college costs.

But the colleges say that, for them, competition has resulted in their prices going up, not down. That’s because of a self-destructive cycle in which they vie for students by offering bigger and bigger discounts they can’t afford — including to families that may not need them. This pushes up the sticker price for everybody else, shifts money away from students who need it most and threatens the very survival of some schools.

If they could talk to each other, college leaders say, they could rein in those discounts. And that would free up money to lower tuition, give more financial aid to students who need it and liberate the institutions from catastrophic bidding wars that are costing them record amounts of money.

“It seems trite to talk about the arms race, but that’s what this is. What we need is a summit meeting. … The alternative is mutually assured destruction.”

“If everyone got into this boat at the same time, then they could drop their tuition. So from a consumer point of view and a public policy point of view, that ought to benefit everyone,” said Richard Detweiler, president of the Great Lakes Colleges Association.

But there would be losers, too: many of the students who now get those discounts.

Related: With consumers pushing back against increased tuition, colleges seek new revenue

For F. M. Scherer, an emeritus professor of public policy at Harvard’s John F. Kennedy School of Government who has focused on antitrust policies, the idea evokes President Harry Truman’s tongue-in-cheek appeal for a one-handed economist.

“This is a case that requires a two-handed economist,” Scherer said.

On the one hand, he said, it’s possible that collaboration could help colleges shore up their increasingly shaky budgets. And that could let them get tuition under control and shift financial aid back to lower-income students.

On the other hand, said Scherer, “It’s just possible that collusion in tuition-setting could be reflected on the cost side by an above-average increase” in the price. “If you relaxed the pressure even more, where would it go? To a general reduction of tuition or to higher educational spending generally on the facilities and staff side? I, frankly, am skeptical.”

So are many Americans, judging from public opinion surveys. Nearly 60 percent of those polled by the nonpartisan organization Public Agenda said they think colleges care mostly about their own bottom lines. About the same proportion in a survey by the think tank New America said colleges and universities put their own interests ahead of the interests of students.

That’s why the few college presidents willing to talk about an antitrust exemption say they are asking for only a limited five-year trial period during which they promise to discuss lowering costs.

“What’s the fear of letting colleges talk to one another? The answer is that there’s a fear of collusion, that you’re going to drive the price up,” said Steven DiSalvo, president of Saint Anselm College. “What if the qualifier was that the conversation takes place within a specified period of time, and only if we’re going to drive the price down?”

About 60 percent of Americans in a survey said colleges and universities put their own interests ahead of the interest of students.

Colleges once talked to each other routinely about cost and discussed how much financial aid to offer individual students who applied to more than one of them. That prevented those applicants from playing financial aid offices against each other for a better deal.

As many as 150 schools belonged to 24 groups that met each spring to compare notes in this way, according to the advocacy organization The Institute for College Access and Success. Then, in 1991, the Justice Department brought charges of price-fixing against the most prominent of these, the Ivy Overlap Group, which included the Ivy League institutions and MIT. The Ivy League schools immediately settled, and the practice largely ended.

Related: Colleges are pushed to stand behind what they sell with money-back guarantees

MIT, however, fought back. A federal court backed the government on the most important question, ruling that the payment of tuition is a commercial transaction subject to antitrust law, even when it’s to a nonprofit university or college. An appeals court mostly agreed, but said MIT made a good argument that there were social and economic benefits to safeguarding limited financial aid. Then MIT settled, too, leaving this issue unresolved.

Since then, colleges have found themselves in an escalating arms race, giving bigger and bigger discounts to fill seats. Small private, nonprofit colleges this year discounted student costs, in the form of financial aid, by an average of 51 cents of every dollar, according to the National Association of College and University Business Officers. And more of that aid went to students who could afford to pay without it.

Students from families earning $155,000 or more a year got an annual average of $5,800 more than a federal formula said they needed, the College Board reports; the figures are from 2011-12, the last period for which they are available, and experts say such discounts have continued to go up since then.

The colleges say this forces them to raise tuition — which the College Board says has grown 13 percent above inflation since 2011 — while still failing to keep pace with costs.

“The game that’s being played is to set your tuition as high as possible and then discount it so that everyone feels like they’re getting a good deal,” said John McCardell Jr., vice-chancellor of Sewanee: The University of the South. “It seems trite to talk about the arms race, but that’s what this is. What we need is a summit meeting. What we need is an arms control meeting. The alternative is mutually assured destruction.”

Critics point out that the colleges could unilaterally disarm. But none wants to go first.

“They can do that without talking to each other. They can make a policy that says we’re not going to give money to students who don’t need it,” said David Bergeron, a senior fellow at the Center for American Progress. “Any of them could decide to do that today.”

That would leave them at a competitive disadvantage, the colleges say. But Bergeron said letting them consult about financial aid and price puts students at one.

Related: Free college didn’t die with the Clinton campaign. It’s just getting started

“It’s a harder case for schools to say they want to cut discounts to avoid the bidding war if there are people who are benefitting from it,” said Jennifer Dowdell Armstrong, an attorney at the firm McDonald Hopkins in Cleveland who specializes in antitrust law.

About two dozen top colleges already have an exemption from Congress to the antitrust restrictions, and are allowed to discuss common ways of calculating financial aid.

But tuition, room and board at those schools didn’t go down during a five-year period studied by the Government Accountability Office; they went up almost twice as fast as at other colleges, and the amount of financial aid given out grew more slowly.

“I struggle to understand why we would insulate one industry without any safeguards because we believe they would go ahead and do good things with all the money they save,” said Barmak Nassirian, a longtime specialist in student aid and director of federal relations and policy analysis for the American Association of State Colleges and Universities — though he emphasized that his opinions were his own and not the association’s.

“I understand the plight of the sector, and I empathize with it,” Nassirian said. “They have gotten into an untenable situation. I’m just not sure that an antitrust exemption is going to fix anything.”

So sensitive is this topic that many higher education organizations wouldn’t discuss it, including the Council for Independent Colleges, or CIC. And there’s another quandary: Even a conversation about having these kinds of conversations can invite an antitrust investigation, as happened after the idea came up at a CIC conference in 2013. The investigation was dropped two months later, but largely ended such discussions.

Most presidents think the current system of discounts for higher-income families runs counter to the goals and values of higher education, but fear they would face litigation if they discussed solutions, according to a survey by the Education Conservancy, which focuses on admissions practices.

“College presidents have really good intentions. And they feel handcuffed,” said Lloyd Thacker, the conservancy’s director and author of “College Unranked: Ending the College Admissions Frenzy.”

The government says that “on the one hand that you have to serve the public interest,” Thacker said, “and on the other that you can’t get together to serve the public interest.”

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