Selection-based Approach to Cooperative Interval Games

Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of the interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterization theorems and relations to existing classes based on the interval weakly better operator. We show new results regarding the core and imputations and examine a problem of equivalence for two different versions of the core, the main stability solution of cooperative games. Finally, we introduce the definition of strong imputation and strong core as universal solution concepts of interval games.