Anime dating sim for iPhone or psp vita?

Is there any dating sim games for iPhone or vita or example like the anime " the world god only knows " it started to interest me: p

There's no such thing as a "PSP vita". There's however a PS Vita.

Persona 4 golden may be what your looking for.

If you want a pure dating sim and not a game with romance elements you won't be able to use your PSVita (unless you are willing to get games in Japanese). I do know of a few dating sims for the iphone though.
-Kira Kira
-MoeCureNet
-Twilight Cherry

Since you are referencing "The World Only God Knows" I'm guessing you want dating sims with a male protag where you pursue females. Next time you should specific though because there are different types of dating sims depending on which gender you want the main character to be and what gender of characters you want to pursue. For example most of the dating sims on the iPhone have a female main character that pursues males.

If you'd like to try finding some of these games yourself the term for a game with a male protag who purses females is " bishoujo game". You can look up "English bishoujo games" on Google or something to find more.

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