Are 3DS games compatible with the DSi & What are good games?

Hi again,

I just want to know if the 3DS games are playable/compatible with the DSi. I have searched the store at my place, but there aren't many games that I like. I'm more of a RPG (Pokemon), Action/Adventure kind of player, so I was looking for some games.

Also, am I able to play 3DS games with my DSi even though it's not in 3D? So that the game is in 2D, but working?