Cooperative Multicriteria Games with Public and Private Criteria; An Investigation of Core Concepts

A new class of cooperative multicriteria games is introduced which takes into account two different types of criteria: private criteria, which correspond to divisible and excludable goods, and public criteria, which in an allocation take the same value for each coalition member. The different criteria are not condensed by means of a utility function, but left in their own right. Moreover, the games considered are not single-valued, but each coalition can realize a set of vectors representing the outcomes of each of the criteria depending on several alternatives. Two core concepts are defined: the core and the dominance outcome core. The relation between the two concepts is studied and the core is axiomatized by means of consistency properties.