He’s moved on but continuously looks for me

My ex and I dated for 4 years. His inconsistency and failure to stick to his promises was the reason I decided to end things. It was a hard pill to swallow but I realized he has a lot of narcissistic tendencies.

We broke up at the end of September and he continued looks for me. He uses different numbers, calls in private, and send numerous messages. He doesn’t get tired. What I don’t understand is every time I give him the opportunity to prove to me why I should give him another chance he shows me why I shouldn’t. He asks to take me out and the day of forgets about it, goes HOURS without messaging me, and has gotten caught in lies. I got stood up 3x. That was enough for me to realize this wasn’t the place for me.

Why does he sickly look for me and lies to me trying to make me believe he wants a life with me, when at the end of the day he doesn’t follow through? What does he gain? Clearly he has a lot of different options so why continuously bother me if I’m not what he wants?

As of now I have gone 2 months without any contact with him. The calls haven’t stopped nor the messages. I see on social media he has moved on so why bother me? What does he gain? Obviously it’s just an ego boost to him but what does he gain if he knows I’m going to cut him off at the first mistake of failure to prove himself?