My 1st answer:
I used to not care about it at all and move on if anything, trying to just get laid. Then I started to realize this fact of competition and it slightly got to me for some period of time when several females were rubbing it in my face, making sure I knew there were other guys pursuing them. Perhaps this was an attempt to get me to move things into a more serious territory or just plain dumb girl behavior.
I have no problem with the reality that other guys are pursuing females. It makes sense because we all want the hottest females and likely will go after the same women. I respect other men's space and don't get butthurt if the girl chooses another guy. She is free to choose whoever she wants. I just expect basic human respect in these matters.
What I have a problem with is the insecure/jealous/envious/overly aggressive guys who do all types of shady sh*t to out compete others. Guys who are willing to get into fights over girls they don't even know. Guys, whose girlfriends have no respect for them and are clearly ready to move on, trying to desperately fend off other men that the girl is interested in instead of letting her go. Guys who see you as competition because you are taller, have more money, more personality, etc and try to tear you down for that without women even being in the picture. Guys who try to copy everything you do, your mannerisms, your speech, your whole life, because they see you as competition and want to get with your women and have zero identity of their own. Another group is the guys who get the chick and then want to rub it in your face in some manner. These men are messing up society and make dating annoying.
Women are free to choose in this day and age. They are free to leave if they want and you shouldn't take it personally. There will always be men who are better than you and women are free to leave you for them if they can/want. Just live your life and be the best version of you.
I also have certain standards where if I know a girl has been with dudes I do not approve of personally, I will end things. This is tricky though because women can hide their past.
My 2nd answer:
It depends on the competition. Sometimes you win and sometimes you lose. I don't like it when a guy is better than me in looks/money/status/etc, and it hurts when women go toward him instead of you. Rejection is painful. However, you can also learn from it. I recently had a chick pulled away from me by a short Indian guy which made me feel like a useless piece of sh*t floating in the toilet bowl. I took a lesson from it though - I should've acted sooner and pulled the chick somewhere instead of standing there and talking to her for so long that she got bored. I've also seen enough women fail to acknowledge my existence when a better looking/taller guy is around me or with me. This can make one swallow the black pill and get depressed. You have to stay away from this negativity though. Women go through this too, however. I actually think they are more aware of their place in their hierarchy than many men are aware of theirs. Again, just live and focus on your own life and be the best that you can be, taking and accepting the women you can get. There is enough p*ssy in this world for you to get what you need.