Optimal strategies in fractional games: vertex cover and domination

In a hypergraph H = (V, epsilon) with vertex set V and edge set epsilon, a real-valued function f : V -> [0, 1] is a fractional transversal if Sigma(v is an element of E) f (v) >= 1 holds for every E is an element of epsilon . Its size is |f| := Sigma(v is an element of V) f (v), , and the fractional transversal number tau(& lowast;) (H) is the smallest possible |f |. We consider a game scenario where two players have opposite goals, one of them trying to minimize and the other to maximize the size of a fractional transversal constructed incrementally. We prove that both players have strategies to achieve their common optimum, and they can reach their goals using rational weights.