What would you say if your greatest, most fierce competitor suddenly retired? Would you praise their accomplishments? Or keep your thoughts to yourself? 

Last week, Roger Federer, one of the greatest tennis players of all time, announced his upcoming retirement. Later that day, Federer's biggest rival, Spaniard Rafael Nadal, released a statement on Twitter and Instagram--and it teaches a powerful lesson for competitors, businesses, and brands everywhere:

"I wish this day would have never come," wrote Nadal. "It's a sad day for me personally and for sports around the world. It's been a pleasure but also an honor and privilege to share all these years with you, living so many amazing moments on and off the court. We will have many more moments to share together in the future. For now, I truly wish you all the happiness with your wife, Mirka, your kids, your family and enjoy what's ahead of you."

Nadal's short statement serves a powerful lesson in emotional intelligence, the ability to make emotions work for you, instead of against you. Let's break down what competitors and business owners everywhere can learn from it. (If you find value in these lessons, you might be interested in my free seven-day course, which delivers a rule to your inbox each day that teaches you how to build emotional intelligence.)

How a good relationship with competitors builds trust--and your brand

Even casual tennis fans are familiar with the relationship between Federer and Nadal.

Longtime rivals and friends, both players have repeatedly credited each other with pushing them to play beyond what they would have done otherwise. Nadal's tweet was just the latest in a long line of compliments both athletes have doled out about each other over the years.

We rarely see this sort of thing in business, though. Imagine a tweet or Instagram post in which McDonald's takes a moment to praise Burger King, or vice versa. Coke vs. Pepsi, Nike vs. Adidas, Apple vs. Samsung--most would immediately describe any of those relationships as completely antagonistic.

But it doesn't have to be that way. A few years ago, when Nintendo launched the Switch (a new gaming system), competitors Sony and Microsoft, creators of the Playstation and Xbox respectively, publicly congratulated Nintendo.

The most interesting part about this? Research shows that public praise of your competition can actually result in increased benefits to your brand.

In one study, researchers showed a group of consumers a fictitious tweet from Kitkat praising competitor Twix: "@twix, Competitor or not, congrats on your 54 years in business! Even we can admit -- Twix are delicious." The researchers then showed a control group a more generic tweet that didn't reference Twix. 

The result? 

"Those who had been shown the tweet in which KitKat praised Twix were 34% more likely to have purchased a KitKat than those in the control group," write the study's authors in HBR. "Importantly, consumers were equally likely to have purchased a Twix regardless of which tweet they saw, suggesting that Twix did not benefit sales-wise from receiving KitKat's praise."

The researchers replicated the study across brands in several industries, including food, ride-sharing, media, and technology. Their findings indicated that "consumers showed greater interest in buying from brands that praised their competitors" and that this effect "was largely driven by consumers' perceptions of a brand's warmth," which resulted in consumers perceptions that a brand was "warmer," i.e., more thoughtful, kind, and trustworthy. This resulted in more engagement with those brands on social media, a reported stronger sense of connection to the brand, and more purchases of the brands' products.

Of course, there are additional reasons to praise competitors. Sincere compliments build goodwill between the compliment giver and receiver, which can lead to further collaboration or partnership in the future. 

In service businesses, praise for competitors can also build goodwill between you and potential clients. It makes them feel "safe," as business expert and author Bob Burg puts it: "'Wow,' thinks your prospect. 'If he/she speaks that well of their competition, I never have to worry about negative things being said about me or any of my staff.'"

Finally, remember this: People like to do business with companies that are authentic, that keep it real. If you recognize that a competitor does something good, if you appreciate something about them, not only is there no reason for you to openly share your thoughts--it's simply the human thing to do.

So, the next time you feel the urge to hold back from complimenting a competitor, remember these two fierce rivals, and their authentic respect for one another. And remember that respect like this is a strength, not a weakness.