Coalitionally Monotonic Set-solutions for Cooperative TU Games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the trade-off between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core- selection requirement by the core-extension property.