Lina Khan, the chair of the Federal Trade Commission, has pledged to usher in a new era of trustbusting of America’s corporate giants, recently saying the agency plans to “enforce the antitrust laws to ensure maximal efficacy.”

Now Ms. Khan has staked that ambitious agenda on a case that may be highly challenging for the agency to win.

The F.T.C. on Thursday sued to block Microsoft’s $69 billion acquisition of the video game publisher Activision, the biggest consumer tech deal in two decades. The action punctuated Ms. Khan’s statements about reining in corporate power and was the boldest of a recent string of lawsuits from the agency to prevent other, smaller deals in the name of competition.

But Ms. Khan and the F.T.C. face hurdles in trying to stop the Microsoft-Activision deal, experts said. That’s because courts have been skeptical of challenges to so-called vertical mergers, where the two businesses don’t compete directly. In this case, Microsoft is best known in gaming as the maker of the Xbox console, while Activision is a major publisher of blockbuster titles such as Call of Duty.

In addition, Microsoft has made a number of concessions to reduce regulatory concerns about buying Activision — such as pledging that Call of Duty would be available on Sony’s PlayStation and Nintendo’s platforms, and not just on Xbox — which some judges may find persuasive.

“It’s undeniably a challenging lawsuit for the commission, because vertical challenges generally have an uphill battle,” said Bill Baer, who led the Justice Department’s antitrust division during the Obama administration and has represented Sony in private practice.

The case is shaping up as a test of Ms. Khan’s belief that the F.T.C. must become more aggressive to check the power of corporate giants in the modern economy, including the biggest tech companies. Appointed to lead the agency by President Biden, she has signaled she wants to take more lawsuits to court — instead of settling with companies — to push the boundaries of antitrust law and return to the kind of trustbusting not seen since the last century.

Since Ms. Khan took over the F.T.C. in June last year, the agency has employed novel or little-used arguments to challenge deals. It sued to block the merger between the chip makers Nvidia and Arm, another deal in which the companies were not direct competitors. In July, the agency sued to stop Meta, Facebook’s parent company, from buying the virtual reality start-up Within, in a case that hinges on an uncommon argument that the deal would harm competition in a market that hasn’t developed yet.

Microsoft has vowed to fight the F.T.C.’s lawsuit against the Activision purchase. On Thursday, Brad Smith, Microsoft’s president, said the company had “complete confidence in our case and welcome the opportunity to present it in court.” On Friday, Microsoft pointed to previous statements that it believes the deal would expand competition and create more opportunities for gamers and game developers.

An F.T.C. spokesman declined to comment on the case.

Regulators have traditionally focused on challenging mergers that combine two direct competitors. When they have brought lawsuits against vertical mergers, their record has been mixed.

The biggest and most bruising recent battle over a vertical merger was in 2017, when the Department of Justice tried to block AT&T’s $85.4 billion purchase of Time Warner. A federal judge ultimately allowed the deal to go forward, saying he was unconvinced the combination would harm competition in telecommunications and media.

This year, a judge ruled against the F.T.C.’s attempt to stop a gene-sequencing company from buying the maker of a cancer blood test, saying the evidence hadn’t proved that the gene-sequencing company would have an incentive after the acquisition to harm competitors of the blood-testing product.

But Ms. Khan, along with her counterpart at the Justice Department, has spearheaded an effort to rewrite the guidelines for assessing such deals.

The F.T.C. has primarily based its case against Microsoft’s Activision deal on the idea that the Xbox and PlayStation consoles compete in a league of their own, and not against other video gaming devices like the Nintendo Switch. Barry Nigro, who worked in the Justice Department’s antitrust division during the Obama administration, said the courts would heavily consider whether that definition was correct in deciding the case.

In its complaint, the F.T.C. argued that the games that Activision made were “extremely important” for the success of video game consoles, so Microsoft would have the ability and incentive to use its control of those titles to keep them from competitors or degrade their quality.

No game is more important to the case than Call of Duty, a first-person shooter game, which the agency called “one of the most successful console-game franchises ever.” Sony has said that if Microsoft got its hands on Call of Duty, it could keep the game off PlayStation, pushing players to Xbox.

Microsoft has repeatedly said it would not make sense to take Call of Duty off PlayStation, where most gamers play the game. This week, Microsoft signed a 10-year agreement to bring the game to Nintendo’s Switch, and has said it offered Sony a similar arrangement.

But the F.T.C. dismissed Microsoft’s promises. It pointed to a $7.5 billion deal that Microsoft closed last year to buy ZeniMax, the parent company of eight game studios that make hit franchises like The Elder Scrolls, Doom and Fallout.

The agency wrote in its complaint that Microsoft had “assured” regulators in Europe who were reviewing the ZeniMax deal that it would not have an incentive to withhold ZeniMax titles from rival consoles. But Microsoft later announced that major new games from ZeniMax’s studios would be released only on its Xbox and Windows computers.

That should “cast more suspicion” on Microsoft’s statements about keeping Call of Duty available on PlayStation, the agency said in its lawsuit.

Microsoft has said those new ZeniMax games cannot be compared to an existing franchise like Call of Duty. It has indicated that the F.T.C. is misrepresenting what happened because the company made no commitments to the European Commission, pointing to European filings in which it said it would decide how to release games on a “case-by-case basis.”

In meetings with the agency and commissioners on Wednesday, Microsoft offered to make enforceable, bound commitments to keep Call of Duty on PlayStation, a person with direct knowledge of the conversations said. But the commissioners did not seem interested in accepting a settlement, the person said.

The F.T.C. declined to comment on conversations it had with Microsoft before the lawsuit.

Those types of agreements have fallen out of favor with regulators like Ms. Khan. She has said promises that companies make to regulators are rarely enforced and don’t address core problems of companies getting bigger and exerting their power to harm competition.

Judges in some recent antitrust cases have cited settlement offers as a reason to allow mergers to proceed over regulators’ objections. “Courts have been surprisingly solicitous about the kind of things that Microsoft has offered here,” said Daniel Francis, an assistant professor of law at New York University and a former F.T.C. official.

The F.T.C. complaint said the first hearing in the case would be in August.

Kellen Browning contributed reporting.

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