The two entrepreneurs have different visions of the future. Still, the fact that both men are possessed by enough self-belief to pull off world-changing feats has earned them a spot in a category of self-centered CEOs, who were first noticed by an anthropologist back at the height of the dot-com bubble. The academic calls them productive narcissists, and he thinks there may be more of them today.
Chief executives are hardly known for being reserved or self-doubting. However, there is something "new and daring" about some of the modern CEOs, said Michael Maccoby, an anthropologist and psychoanalyst who first wrote about this new type of leadership in an article for the Harvard Business Review more than a decade ago.
Called "Narcissistic Leaders: The Incredible Pros, the Inevitable Cons," the article noted that corporate chiefs like Apple's deceased CEO Steve Jobs, Amazon's Jeff Bezos and Microsoft co-founder Bill Gates were "transforming" industries with their ability to be "gifted and creative strategists who see the big picture and find meaning in the risky challenge of changing the world and leaving behind a legacy."
Anthropologically speaking, this particular group also appears to be thriving in ways that set them apart from their peers in the business world. Facebook and Tesla Motors did not immediately reply to CNBC's request for comment.
"I think there may be more productive narcissists today, visionaries trying to change the world," Maccoby told CNBC in an interview. It's the productive narcissist, he explained, who will "solve problems and meet needs" in areas like energy, the environment and national security. "We need visionaries."
More often than not, the term narcissism evokes the personality disorder variety, defined by the Diagnostic and Statistical Manual of Mental Disorders—the bible of the American Psychiatric Association—as "self-centered or egotistical behavior that shows up in thinking and behavior." Yet Maccoby's version of of productive narcissism functions as something like a term of endearment, and comes with tangible accomplishments. Narcissism can actually be "extraordinarily useful" and "even necessary," Maccoby states.
Productive narcissists, he describes, are "visionaries" who want to change the world, are extremely competitive and aggressive, have little respect for the rules that others follow, and tend to use people who serve their purpose.
Bezos, co-founder and chief executive of Amazon.com, Maccoby said, is a productive narcissist who is now joined by, among others, the CEOs of Facebook and Tesla Motors. "Elon Musk is a classic productive narcissist," he said.
Musk, indeed, has an animating vision he'd like to see brought to life. More specifically, he's dreaming of a more energy efficient world. Last year he opened Tesla's patents to rivals "for the advancement of electric vehicle technology," and this year he introduced a new line of solar-powered batteries for the home and office.
However, the SpaceX co-founder also has another vision that is, quite literally, out of this world: the colonization of Mars. "There is a strong humanitarian argument for making life multiplanetary," Musk told Aeon Magazine last year, making the case for needing to safeguard mankind's existence if "something catastrophic" were to happen.
"Whatever skeptics have said can't be done, Elon has gone out and made real," Richard Branson, founder of Virgin Group, wrote about Musk for Time magazine. "Elon is working to improve our planet," Branson added, and "is clearly a man who can see many things at once."
Similarly, the chief of the world's largest social network seems to have a grand idea of how the world of tomorrow should function. In a Facebook post last year, Zuckerberg expanded on his vision to "connect the whole world" through his Internet.org initiative.
"We've been working on ways to beam Internet to people from the sky," he wrote, which includes tinkering with drones, satellites and lasers. The initiative has already connected people in Tanzania, Kenya, Ghana, Zambia, Colombia, Malawi and India, according to its website.
Zuckerberg's vision, however, has been met with some resistance. In India, critics have attacked the idea as distorting competition, while Wall Street analysts wonder what value the initiative brings to Facebook's investors.
However, Zuckerberg—like other productive narcissists—"tend[s] to ignore doubts and criticism," said Maccoby, which doesn't come without its risks.
"The danger is that narcissism can turn unproductive when, lacking self-knowledge and restraining anchors, narcissists become unrealistic dreamers," he added.
Empirical data show that the jury is still out on whether a narcissistic executive can deliver for his company rather than promoting his own self-interested vision. Indeed, the road is littered with CEOs with grandiose plans who failed to deliver shareholder value, or boost their company's fortunes.
A 2014 study by the University of Southern California found that, while narcissistic CEOs generated higher stock prices and earnings per share, their "behavior can be detrimental to a company in the long term."
A separate study by researchers at the University of Maryland and the University of North Carolina, said that narcissism was generally a "bad sign"—exemplified mostly by the size of a CEO's signature. That, the study said, was thought to be an indication of overconfidence that "predicts an array of negative outcomes," including overinvestment, fewer patents and lower return on assets. Nonetheless, the study added these same CEOs earned more than their peers.
"There are many people who are egoists and self-promoters who are not productive narcissists," Maccoby said, especially now amid the ubiquitous hashtags and status updates of social media. Without naming names—although these CEOs, perhaps, know who they are—Maccoby asserts that "social media is bringing out these self-promoters."