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.
A few weeks ago, I saw a young boy riding his bike in the street at a busy intersection. When he rode slowly by, I said, 'Excuse me, young man -- be careful, this is a busy intersection; maybe you should ride on the sidewalk.' He was no bigger than a third grader -- how he responded was quite disturbing to say the least.