On two theorems of positional games (Q2416496)

The author widely discusses some version of positional games called \textit{Maker-Breaker games}, defined by the following: Let $(V,\mathcal{F})$ be an arbitrary finite hypergraph. Here $V$ is a finite set, called the board of the game, and ${\mathcal{F}}$ is an arbitrary family of subsets of $V$, called the family of winning sets. The two players, ``Maker'' and ``Breaker'' alternately occupy previously unoccupied elements of the board $V$. Maker's aim is to claim every element of a winning set $A \in {\mathcal{F}}$, and Breaker's aim is to prevent Maker from doing so. The winner is the one who achieves his goal (a draw is impossible). The paper gives a review of the results about such games and completes two of their proofs.