Definition from Urban Dictionary by ( oldman Feb 17, 2008) : "yandere" - Contrary to the popular belief that it is the opposite of tsundere, it describes an anime character who is either psychotic or violent or both, and shows affection to the main character. Became a popular moe genre after the airing
of the last episode of School Days. Other yandere characters include Ryuuguu Rena from Higurashi No Naku Koro Ni series.
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There are many games with yandere characters, but how many games have you seen where you get to play as a "Yandere".
Perhaps you play as the "good voice" in a yandere's head (e.g. a symbiotic organism in the yandere's brain whose aim is to stay alive), preventing him/her from murdering anybody who may potentially be a rival love interest to your crush.
Maybe there is stats such as "psycho" meter, as well as "happiness" meter that you have to balance, to avoid her from murdering others or committing suicide.
It would be interesting to see how far you can prevent her from getting unhinged by events, of which the most mundane events may be the difference between her staying out of jail or murdering the entire town to 'protect' her crush.