Microsoft, the technology giant that ranks as one of the world’s most valuable companies, has been shaken by the upheaval at OpenAI, the small but influential artificial intelligence start-up that was founded as a nonprofit and developed the ChatGPT chatbot.

The unexpected ouster on Friday of Sam Altman, OpenAI’s co-founder and chief executive, set off a chain of events that erased tens of billions from Microsoft’s market value, a sign of how important OpenAI is to the tech behemoth. Microsoft has invested more than $13 billion in OpenAI, and Apple, Google and Meta have rushed to catch up with their own A.I. offerings.

Microsoft’s stock has been on a roller coaster since Mr. Altman’s departure from OpenAI, dropping on Friday and continuing to slide in after-hours trading. The decline of more than 2 percent translates into an enormous loss of value for a company with a market capitalization approaching $3 trillion.

Microsoft’s stock price served as a referendum of sorts on its partnership with OpenAI. Microsoft led an effort over the weekend to try to convince OpenAI’s board to reinstate Mr. Altman, a charismatic, well-connected founder in Silicon Valley who at that point was also pitching a new A.I. start-up to investors.

In the end, Microsoft said late on Sunday that it would hire Mr. Altman and Greg Brockman, OpenAI’s president and a company co-founder who quit in solidarity with Mr. Altman. The two men will lead an advanced research lab at Microsoft, “setting a new pace for innovation,” according to Satya Nadella, Microsoft’s chief executive.

Microsoft’s stock rose in choppy premarket trading on Monday, recovering much of its previous decline. Analysts praised Microsoft’s move to hire the OpenAI outcasts.

“We think Mr. Nadella may have pulled off his own coup, acquiring the most important part of OpenAI: its ambitious talent,” analysts at Macquarie, a bank, wrote in a research note.

OpenAI named its second interim chief executive in as many days, tapping Emmett Shear, the former chief executive of Twitch. Mira Murati, a longtime OpenAI executive, was initially made interim chief after Mr. Altman’s departure.

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