I agree you should not participate in this. I doubt, however, that most bosses who create this sort of environment will listen to any concerns you express about it. My advice would be to find a more hospitable workplace.
John N. Frank
It’s demoralizing to have a boss who pits you against your colleagues. Don’t give in to this dynamic. Instead, collaborate with coworkers to find your own ways of working together that don’t ratchet up the competition.
Tell your boss how you feel about the situation, but be diplomatic and constructive. If she thinks you’re complaining, she won’t take your concerns seriously. Discuss it with your colleague(s) first and then meet with your boss, perhaps together. Say you’d like to stop vying for the spotlight, because it’s distracting you from doing your best work.
Ask if she can avoid putting you in competitive situations (and give a few examples, in case she’s not tuned in to her own behavior) so you can both be more productive—to the benefit of all.
Adapted from the HBR Guide to Office Politics.