Los Angeles is all but guaranteed to get the Olympic Games. The question is when, 2024 or 2028?

Los Angeles is all but guaranteed to host the Summer Games for a third time after Olympic leaders made the unusual decision Tuesday to name two winners in the bid race between L.A. and Paris, giving 2024 to one city and 2028 to the other.

After the historic vote by International Olympic Committee members gathered in Switzerland, one key question remained.

Can the cities agree on who goes second?

“We’re one step closer to making it happen,” L.A. Mayor Eric Garcetti told reporters at a news conference in Lausanne. “I have full confidence we will get there.”

Even though his counterpart, Paris Mayor Anne Hidalgo, expressed similar optimism, the French have repeatedly dismissed the idea of waiting another four years. It has been widely speculated that L.A. bid leaders — who have been more flexible on the issue — will seek financial or other concessions in return for accepting 2028.

But if the IOC, L.A. and Paris cannot reach an accord, the final selection in mid-September will revert to a winner-take-all vote for 2024 only.

“We take nothing for granted,” Garcetti said. “Our job now is to work with the IOC, to forge a path forward for our city and for the future of [the Olympic] movement.”

The IOC convened this week’s session amid growing concerns about the massive cost of staging the Games.

Estimates for the 2014 Sochi Winter Olympics — though admittedly inexact — have ranged past $50 billion. Rio de Janeiro was left with a reported debt of $35-$40 million from the 2016 Summer Games.

In the 2024 race, Boston, Budapest, Hungary, Hamburg, Germany, and Rome backed away in response to public opposition, which IOC President Thomas Bach has labeled as the “new political reality.”

With L.A. and Paris showing support in local polls and insisting they can ease costs by using existing stadiums and arenas, Bach decided his organization might do well to secure both simultaneously.

Tokyo has already been awarded the 2020 Summer Olympics. By naming locations for subsequent two Summer Games, the IOC could buy itself more time to make hosting more affordable and to attract more bids.

Preceding Tuesday’s vote, bid teams from each city gave a presentation of their plan to the membership. France brought along newly elected President Emmanuel Macron.

President Trump did not attend, but tweeted: “Working hard to get the Olympics for the United States (L.A.). Stay tuned!”

IOC members debated the two-winner proposal after lunch, then gave their unanimous approval. Garcetti and Hidalgo appeared unexpectedly on the dais.

“Thank you,” Hidalgo said.

Garcetti added: “Can we just say thank you?”

The mayors summoned Bach to join hands in a salute. The IOC president later said: “Ensuring the stability of the Olympic Games for 11 years is something extraordinary. This is why we think that today, this is a great day for the Olympic Games and the Olympic movement.”

Though there had been some preliminary negotiations involving both cities, the real work was set to begin as early as Tuesday night when the mayors were scheduled to dine with Bach.

In an interview with The Los Angeles Times last week, the IOC president expressed his desire to reach a tripartite agreement before the official selection in Lima, Peru, later this summer.

“I just hope in August we could be there if everything is going well,” he said.

The sticking point for Paris 2024 could be a plot of land in Seine-Saint-Denis where officials would construct an athletes village. The location cannot remain undeveloped for four more years, they have previously said. Their plans also call for building a swim arena and media housing.

By comparison, L.A. — which hosted the Games in 1932 and 1984 — would rely almost entirely on such facilities as the Coliseum, Pauley Pavilion and Staples Center. UCLA would house athletes and USC would accommodate the media.

A switch to 2028 would require adjustments to all the venue agreements. The Los Angeles City Council, which had previously approved a 2024 bid, would need to revisit the plan.

“We’ll take whatever actions need to be taken,” Council President Herb Wesson said. “At this point, I don’t see any hang-ups.”

The same may not be true for potential IOC concessions.

The U.S. and France have lost a string of bid attempts in recent years, so it remains to be seen how hard they will push. Paris has appeared particularly eager to host 100 years after their most-recent Games in 1924.

Bach has downplayed the prospect of linking enticements to 2028, saying recently: “I don’t think you need to reward somebody if you give somebody a present.”

But Garcetti has mentioned IOC funding for youth programs in the city. LA 2024 could ask for money to remain in operation an extra four years or could seek a larger slice of Olympic revenues.

“We’ll sit with our team, Paris will sit with their team,” Garcetti said. “We will look at our options.”

david.wharton@latimes.com

Follow @LAtimesWharton on Twitter