On the existence of values for arbitration games

Two-person games in normal form are considered, where the players may use correlated strategies and where the problem arises, which Pareto optimal point in the payoff region to choose. We suppose that the players solve this problem with the aid of an arbitration function, which is continuous and profitable, and for which the inverse image of each Pareto point is a convex set. Then the existence of values and defensive ε-optimal strategies is discussed. Existence theorems are derived, using families of suitable dummy zero-sum games. The derived existence theorems contain all known existence results as special cases.