Rich Extensions of the Core and the Equal Split Off Set

Abstract

This paper studies extensions of the core and the equal split off set (ESOS) for TU games, and also subsolutions of the extensions in order to derive some new egalitarian solutions for TU games. Stability of the allocations is weakened such that an allocation [Formula: see text] can be blocked only by rich coalitions which together with a player will contain all players having payoffs not less than him. In accordance with such a definition of blocking, two new solutions — the rich core and the egalitarian rich core — are defined and characterized by means of weakening of axioms characterizing the ESOS on the class of all TU games [Dietzenbacher, B. and Yanovskaya, E. [2021] Consistency of the equal spit-off set, Int. J. Game Theory 50(1), 1–22]. Two subsolutions of the egalitarian rich core — the set of Lorenz undominated allocations and the set of allocations that lexicographically minimize maximal payoffs of players (Lmax solution) are characterized. The tight upper boundary of the number of allocations in the ESOS and in the egalitarian rich core is found.