Are INTPs generally competitive

Turn yourself into a project or study of N=1. I did that and I am slowly learning to control my worst personality traits.

Then it all comes down to testing your theories (in this case: about yourself). For an INTP this means putting in some harder work; going out is one of the things you'll need to do.

For example: against depression I arm myself by training my body: I exercise (weight training/running/body weight training) during the week, I consider sleep to be my most valued good, I use fasting to control my body weight etc... (studies have shown it helps your mind a lot when your body is fit; I used to be in my mind too often to notice my body decaying) During running I listen to audio books or do some thinking. I keep a notepad with me at all times. I take note of my progress in what I do, because I think training is boring, but making graphs about my progress engages me to do the work.

For social interactions I did a similar experiment. I went to clubs/bars/cafés by myself. And started noti(ci)ng how other people interacted with eachother. IF you go by yourself you are in a severe disadvantage: you'll be the odd one out. So what I do now if I go somewhere where I do not know anyone is this: I smile; I say something to the very first person I come across (the interaction doesn't last more than a minute: eg "there is a police control going on further down the road", it doesn't have to be true), the point of this is that other people in the venue will have seen me interacting with the person, which makes me appear less alone, less odd, etc...; then I typically order a drink I talk to the bartender or people who are also waiting for a drink (this conversation needs to be highly casual+ make eye contact+keep smiling+if someone is rude to you ignore it and turn away; never engage with someone more than a few minutes); if you get your drink keep moving around; if you start noticing your energy going down or start feeling alone, go out once, return and repeat; if you lost your mojo, leave (the key is to not let other people notice that you are feeling insecure: by moving around a lot and talking you can accomplish this): the important thing is with this exercise (and it is an exercise) is that you learned something= 'you can interact with other people'. It will not be on the level you want to, but that is not necessary... See it as a tool you can use to get out, feel less alone and socialise. It might happen that some of the people you meet will stick to you and you may become friends. To me it is very important to analyse who those people are... if they are bad news, ditch them, you do not need them.

For deeper and more meaningful conversations: Go to the local library and see if they organise book clubs or philosophy courses/gatherings/cafés. Consider it also an exercise to participate in these things. People who tend to go to these things most of the time also feel a need to talk about deeper issues. You could also consider adult classes on any topic. You'll learn to do something new and you can interact with other people doing the same thing.

By going to such events you can control your need to be alone. If you want to be by yourself, you simply skip a class or an event.

To me friends are overrated: some are too clingy, too obnoxious, too self centered, etc... By constantly meeting new people, you can socialise without too much interaction with your normal life. You can always choose, however, to make real friends and introduce them into your life. It is important however to always set your boundaries for yourself.

To change the world you need to learn how to influence people. This is a hard cookie to crack for an INTP, but the above exercises should be a start. Communication is most important to make some real impact on what happens. I suggest reading books about Malcolm X, JFK, Abraham Lincoln, Martin Luther King, etc... Learn to write speeches and apply them to a live audience, maybe even go to a ToastMasters gathering.

If you do the work, you will get there eventually.