If I stop undermining her, will she continue to undermine me, which puts me at an overall disadvantage?
A: It's not unusual for a management team to have a pair of rivals in it. Teams can be a lot like a family, with the leader in a parental role and sibling rivalry between the more junior members, each vying for attention. Though not uncommon, this kind of competitiveness is unhelpful to team effectiveness, with negative energy being expended by the two rivals in a futile struggle, but also by the rest of the team in trying to ignore the situation or ameliorate it.
Often, what's behind it is insecurity and lack of confidence. This can be brought about by a particular situation where limited opportunities are up for grabs, so there is a legitimate cause for competition. However, for some people, it's a way of life that has probably been with them since childhood.
Ask yourself if you have been in such a situation before - not necessarily at work. If so, it's worth trying to get grips with it before you harm your professional and personal relationships.
This is a particular kind of 'racket' described by Thomas Harris in his classic book I'm OK, You're OK. Among other useful ideas, he suggests that in our interactions with others we can get ourselves into patterns where we feel good about ourselves - OK - only when we can point to someone else not being OK. In your case, both of you have a personal investment in the other being 'not OK'. If both of you really felt good about yourself, secure in your job and appreciated in your work, there'd be no need to engage in this battle.
Between you, you've set up an unhealthy cycle in which one of you does something and the other retaliates, on and on in a continuum. The only way to stop it is for one of you to break the chain. Since you are the one aware of this cycle, it had better be you.
How do you go about breaking the habit? Stop giving precious energy to thinking about your colleague negatively. Start acknowledging her strengths.
Give her some positive attention. If she feels appreciated and not under attack, she may relax and reciprocate. If she doesn't, she may nevertheless get bored when you stop playing the game. If she continues to behave immaturely, she will show herself in a bad light.
Of course, there are other ways of making oneself look better than making someone else look worse. Working out what your strengths are and playing to them is one; developing some genuinely relevant and differentiating talent or knowledge is another. If you were to focus some energy away from the goldfish bowl that is your management team, to think about the wider world of your marketplace or the industry in which you work, you might well gain a perspective that would benefit your organisation and thereby your own chances of advancement.
What about your concern that if you stop behaving competitively she might get ahead? Frank Dix, former Olympic team coach, says having competitors is a good thing: your competitor lets you know what you've got to beat, and so brings out a better performance in you.
Use this thought to evaluate yourself. Are you as competent as she is?
As experienced? Is the state of your relationship with your boss and team members as good? Is there anything positive you could learn from your rival? And how do you both compare to your peer group? When you take a long, honest look at yourself, you may find gaps between where you are now, in terms of professional attributes, and where you need to be. This will give you a direction for your development and a healthier focus for your energies.
A key differentiator between you could be attitude. If I were your boss and had to choose between two competent people, one of whom has accepted that there are other talented people on the team and found productive ways to work with them, and the other who is forever bitching about her rival and trying to promote herself, my choice would be pretty clear. If neither person had this positive attitude, I'd look elsewhere - possibly outside the organisation.