Mirai Nikki (TV), Accel World Recommendations
The art styles of both Anime contain Gothic elements. The story lines are dark. The main characters are nobodies. Technology is in some manner involved. A game is involved that could leave one completely out of the game for good. Things slowly get revealed over time. They also have interesting casts of characters.
Both male protagonists get caught up in a game challenging other player, as well as female characters leading them along the journey. The protagonists have a goal to find out their identities, and defeat the other players to win the game. However Mirai Nikki is more violent and gory since players are killed when defeated, while Accel World is just action.
On one hand you have an insane yandere, and on the other hand you have a deredere.
Look past the basic cast and setting and you'll see many similarities between the show.
Weak main character with a strong heroine and useful friends.
Battle royale - kill or be killed, kill everyone else to achieve limitless power.