Towards an axiomatization of the core-center

The core-center is an allocation rule introduced in González-Díaz and Sánchez-Rodríguez (González-Díaz, J., Sánchez-Rodríguez, E., 2007. A natural selection from the core of a TU game: The core-center. International Journal of Game Theory 36, 27-46. doi: 10.1007/s00182-007-0074-5) for the class of games with a non-empty core. In this paper we present a weighted additivity axiom, which we call trade-off property, and use it to obtain two characterizations of the core-center.