It is played by two players, called Balancer and Unbalancer.
is balanced, i.e., the elements in each set are distributed roughly equally between the players.
Formally, the goal of balancer is defined by a vector
Balancer wins if in every set i, the difference between the number of elements taken by Balancer and the number of elements taken by Unbalancer is at most bi.
[2] In a Maker-Breaker game, Breaker has to take at least one element in every set.
In an Avoider-Enforcer game, Avoider has to take at most k-1 element in every set with k vertices.