Like in Pikmin 2, Pikmin 3 has a 2-Player Battle mode called Bingo Mode. The overall rules have changed, but many of the same concepts return. The mode can be played in 1vs1 or 2vs2.
Maps
These are 2 of the maps revealed for Bingo Battle so far...
Basic Rules
One player will play as Alph, while the other will play as Captain Olimar. On the bottom of each player's screen, there will be a 4x4 bingo card with random objects, which range from enemies to fruits to treasures. The player that collects all of the objects in a row, (horizontal, vertical, or diagonal) will win, similar to bingo.
Pikmin
Unlike in Pikmin 2, each player can have any type of Pikmin. The only difference is that the color of the Pikmin's leaves, buds, or flowers will correspond with the player. (Player 1: Blue. Player 2: Pink).
Controls
Similar to Pikmin 2, this game mode involves 2 Players using the Wi Remote Plus and Nunchuck (or possibly a pro controller). Most standard controls apply, but down on the D-Pad now activates items. The Gamepad serves as a map and can show where either player is.
Items
Once again, the player can get items by carrying back Cherries back to the assigned onion. Returning items include Pikmin + Items (+5, +10), and the Rocks to fall from the ceiling. A new items seems to act as lightning, as seen in the picture below. It stuns the captain and pikmin for a short amount of time. One can hold a maximun of 5 cherries.