On the set coincidence game

Abstract In the Set Coincidence Game G ( V , W ), two players alternately choose elements not previously chosen from a finite, nonempty set V , and W is a given family of nonempty subsets of V (the ‘winning sets’). The winner is that player who first adds an element to the set of ‘chosen’ elements S , so that S ∈ W . This game is closely related to and generalizes Ringeisen's Isolation Game on graphs. We develop the theory of G ( V , W ), present and support a conjecture about the structure of minimal forced wins, and then prove a weakened form (the Weak Filter Theorem). It is hoped that the indicated themes about optimal design of forced wins will prove of interest for a variety of combinatorial games.