Lorenz-maximal solutions for games with a restricted cooperation

Cooperative games with a restricted cooperation, defined by an arbitrary collection of feasible coalitions are considered. For this class the Equal Split-Off Set (ESOS) [1] is defined by the same way as for cooperative games with transferable utilities (TU). For the subclass of these games with non-empty cores the Lorenz-maximal solution is also defined by the same way as for TU games. It is shown that if the ESOS of a game with a restricted cooperation intersects with its core, then it is single-valued and Lorenz dominates other vectors from the core, i.e. it coincides with the Lorenz-maximal solution.
Cooperative games with coalitional structure for which the collection of feasible coalitions consists of the coalitions of partition, their unions, and subcoalitions of the coalitions of the partition, are investigated more in detail. For these games the convexity property is defined, and for convex games with coalitional structure existence theorems for two egalitarian solutions – Lorenz maximal and Lorenz-Kamijo maximal – are proved. Axiomatic characterizations for both these solutions are given.