I've had a DSi for almost an entire year now, and on May 20th of this year, Nintendo discontinued WiFi and multiplayer matchmaking on games.
As of May 20, 2014, certain online functionality offered through Nintendo Wi-Fi Connection is no longer accessible. The discontinued services include online play, matchmaking and leaderboards for many Wii, Nintendo DS and Nintendo DSi games.
However, as far as I know, the Nintendo 3ds has WiFi functionality. If I played Mario Kart DS on a 3DS, would I be able to play multiplayer Mario Kart DS, or are the services discontinued for the entire game?