Discrepancy game

Summary

A discrepancy game is a kind of positional game. Like most positional games, it is described by its set of positions/points/elements ($X$) and a family of sets ($\mathcal{F}$- a family of subsets of $X$). It is played by two players, called Balancer and Unbalancer. Each player in turn picks an element. The goal of Balancer is to ensure that every set in $\mathcal{F}$ is balanced, i.e., the elements in each set are distributed roughly equally between the players. The goal of Unbalancer is to ensure that at least one set is unbalanced.