A solution to the Box Game (Q1095050)

The authors give a complete solution to the Box Game introduced by \textit{V. Chvátal} and \textit{P. Erdős} [Ann. Discrete Math. 2, 221-229 (1978; Zbl 0374.90086)]. This is a two player game played on n pairwise disjoint nonempty sets \(A_ 1,...,A_ n\). At each of their moves the players, called the Maker and the Breaker, claim at most q resp. p elements from the sets. The objective of the Maker is to claim all elements from one of the \(A_ i's\), while the objective of the Breaker is to prevent him to succeed.