Section 2 of the Sherman Act provides: 

Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce among the several States, or with foreign nations, shall be deemed guilty of a felony, and, on conviction thereof, shall be punished by fine not exceeding $100,000,000 if a corporation, or, if any other person, $1,000,000, or by imprisonment not exceeding 10 years, or by both said punishments, in the discretion of the court.

The Washington Examiner, among other outlets, reports that President Obama and former Republican presidential candidate Mitt Romney are fighting a section 2 lawsuit together.  The lawsuit, filed by a group of  third-party political groups including the 2012 nominees for the Libertarian Party and the liberal Green Party, claims the Commission on Presidential Debates committed antitrust violations:

This action challenges a per se continuing illegal conspiracy or agreement between the RNC, the DNC, and the Commission, with the direction, assistance, and collusion, over the course of many years, of several co-conspirators and affiliated persons, including Fahrenkopf, McCurry, Obama, Romney, and other presidential candidates of the Republican and Democratic Parties. The conspiracy commenced prior to the formation of the Commission, and no Defendant has withdrawn or abandoned it. The overall objective was and continues to be the entrenchment market power in the presidential debates market, the presidential campaign market, and the electoral politics market of the two major political parties by exercising duopoly control over presidential and vice presidential debates in general election campaigns for the presidency. That objective was achieved in 2012 when the individual Plaintiffs were arbitrarily excluded substantially because of hostility towards their political viewpoints from presidential and vice presidential debates between the nominees of the two major parties organized and conducted by Defendants on October 3, 2012, October 11, 2012, October 16, 2012, and October 22, 2012, respectively.

Romney's brief responds:

Presidential debates are a quintessential political, non-commercial activity… .

The antitrust laws were not intended to regulate non-commercial markets like the 'marketplace of ideas' (even assuming such 'markets' exist as anything more that metaphors). Plaintiffs' claims therefore fail. . . . .

Soliciting votes is fundamentally different from selling widgets. The former implicates core constitutional values that are absent from the commercial arena. The First Amendment forbids Congress from telling political candidates where to go, what to do, what to say, or— crucially here—who they have to debate. Just as President Obama has an absolute right to refuse to debate every person who attacks his Administration, Governor Romney had an absolute right during the 2012 presidential campaign to refuse to debate Gary Johnson, Jill Stein, or any other candidate waging a long-shot bid for the presidency. The only possible sanction for that refusal is a political one.

I'm not an antitrust expert, but this case seems like a loser even if the concept of the claim is viable.  The Examiner piece quotes an expert, Geoffrey Manne, executive director of the nonpartisan think tank International Center for Law and Economics, who said the case was out of the ordinary, but not inconceivable: 

"The short answer is that it is not crazy… The commission is a private entity, not a government one, so it doesn't get immunity," he said, adding, "The question is whether the activity amounts to a restraint of trade." It was hard to tell how a court might come down on that, he said.

Manne knows his stuff, and I trust his point that the claim could have legs. I also agree a court might buy it.  Still, I think it ultimately fails in most courts. It seems to me that it is reasonable to have some limits on who participates in debates (do we all get stage time?), and because of that, plaintiffs would likely have to show that the current structure is an unreasonable restraint on trade. Then you start getting into where to draw those lines, and I think you have a problem with the marketplace. That is, not all speech is being shut out, and two people don't have to agree to share a platform with others.  

Furthermore, if people cared, CNN or FoxNews or TruTV or HBO, could have debates with the other candidates and invite all of them.  I'd argue they should.  But the fact that people don't vote with their eyeballs suggests the restraint isn't really as simple as the debate commission.  It's a lack of interest.  I'd like to see a broader discussion of ideas – maybe a real platform of people who think government should be inclined to stay out of bedrooms and boardrooms, for example.  But I don't think the Commission on Presidential Debates is really responsible for the nation's inability to demand more information, more interaction, and more accountability.  

Maybe in 1976 or even 1986, but not in 2016. There's just too many options for the other candidates to get their word out if the people care.  People should care, but I don't think antitrust law was designed to make that happen, nor do I think it can.