A positional game is a two-player game with perfect information played on a hypergraph 
. The players alternately claim previously unclaimed elements of the board 
, and the hyperedges are the
winning sets (Kruczek and Sundberg 2008, p. 1).
In a strong positional game, the first player to occupy every element of a winning set wins. In a Maker-Breaker game, Maker tries to occupy a winning set, while Breaker tries to prevent this (Kruczek and Sundberg 2008, pp. 1-2).
