I want to start a new manga that has some psychological warfare just like in death note and liar game( An anime will be good too)......
I will try and tell u how i think about Majin Tantei Nougami Neuro Thx though i have already mirai nikki and enjoyed it a lot
no usogui doesn't have an anime and neither do any of my other recommendations. But Kurosagi does have a live action tv show, which I have heard is quite good, and it has more romance, which not sure is a plus for you or not. I don't know how much it's based off the manga, since I have not seen the show yet, but I plan too watch it. If you don't mind subtitles than I would say you should watch it (based off the reviews I have read so far).
Bloody Monday has a dorama. Particularly i like it, it doesn't exacly follow the manga if I remember right, but it's quite nice.
Ah... ana no mujina might be potentially like that. Though the demographic is shounen. Alice in borderland might be interesting. Though, there is a lot of recommendation if you go to baka updates, I think.