In many share problems there is an a priori given a natural set of possible divisions to solve the sharing problem. Cooperative games related to such share sets are introduced, which may be helpful in solving share problems. Relations between properties of share sets and properties of games are...

Inspired by Kalai-Samet [4] and Tijs [11], weighted average lexicographic values are introduced for share sets and for cores of cooperative games using induction arguments. Continuity properties and monotonicity properties of these weighted lexicographic values are studied. For subclasses of...