Core bound reduced games and consistency

The lower and upper exact core bounds describe the minimum and maximum individual payoffs within the core of a balanced game, respectively. Based on these bounds, we introduce lower and upper core bound reduced games and study the relation with other reduced games. We axiomatically characterize new solutions for balanced games as unique core bound consistent extensions of the classical two-player principles of unanimity, standardness, and constrained egalitarianism. We name these solutions core covers, equal gap values, and constrained equality values, respectively.