Waiter–Client game

Summary

A Waiter-Client game (also called: Picker-Chooser game) is a kind of positional game. Like most positional games, it is described by its set of positions/points/elements ($X$), and its family of winning-sets ($\mathcal{F}$- a family of subsets of $X$). It is played by two players, called Waiter and Client. Each round, Waiter picks two elements, Client chooses one element and Waiter gets the other element (similarly to the Divide and choose protocol).