Tuza Zsolt: Fractional versions of combinatorial games

In this joint work with Csilla Bujtás we introduce and study the fractional
versions of some competitive combinatorial games, in particular the graph
domination game and the hypergraph transversal game. In the "integer" games
two players alternately select vertices until a dominating set or a vertex
cover is obtained; one of the players wants to finish the game quickly while
the other player wants to delay the end. We consider the variant where the
players have the option to assign a unit weight step by step in fractions
to a finite or infinite sequence of vertices. Fundamental properties of this
new game are proved, for example the existence of an optimal strategy for
each player.