By pausing and offering a genuine compliment, you invite a two-way experiment in vulnerability, both to you and whoever is giving or receiving the compliment. It's one thing to ask for a compliment. It's another to receive it fully without deflection. When we are vulnerable we let our guard down to connect and fulfill one of our deepest human needs.
When your colleague does a great job on an important project, compliment them on their success. If your competitor got the job over you, send a note of congratulations. Drop your guard, put down your competitive armor, and give yourself permission to revel in someone else's success. Make your words strong and reliable.