First, let me say, that I really dislike the word ego. I think it's thrown around too much. In most cases when the person really does have an inflated ego, he/she isn't threatened by anyone, because by definition, Egomania: Excessive vanity, pride or arrogance. To be overly taken with ones own importance, doesn't allow them to care about you.
Usually what's going on is not egomania, but plain old simple insecurity. When someone doesn't feel completely confident about his/her abilities, job security, knowledge, etc, they feel easily threatened.
You can't control other people's insecurities, however you can do your best to put their minds at ease. If you pick up on the signals that they feel threatened, go out of your way to:
1. Ask them what you can do to help them.
2. Go the extra mile; see what they eat or drink from the craft service table and bring it to them when it looks like they can use a break.
3. Make it clear that you are there to support them and make them look good, and are ready to take their direction.
4. When you are given praise by the higher ups, acknowledge your fellow crew members and tell them what a great team they've put together.
It's not for you to make yourself small so that others can feel better about themselves. It's for you to be at your best so that others can shine along with you.
For more tips and advice by top entertainment industry career coach, The Greenlight Coach, visit www.TheGreenlightCoachBlog.com