Disambiguation: for the series itself, see Deca-Dence.
A gigantic 3000m-high mobile fortress created by humans to counter the Gadoll.
The name spells out "Decadence", reflecting humanity's almost doomed state at the attacks of the Gadoll.
The Deca-dence is also the name of the game the cyborgs play and when they log in, they receive an Avatar in the fortress. Using that avatar, they can fight Gadolls.
After the destruction of the Deca-dence, the machine became a city called Deca-dence City and new areas and hobbies, from farming to battle arena, were introduced for the cyborgs to entertain themselves while living with the humans.