Essays on egalitarianism-based solution concepts for cooperative TU-games

Identifier:  TDX:2707

Handle: https://hdl.handle.net/20.500.11797/TDX2707

Authors:  Mauri Masdeu, Llúcia

Abstract:
For a class of reduced games satisfying a monotonicity property, we introduce a family of set-valued solution concepts based on egalitarian considerations and consistency principles, and study its relation with the core. Regardless of the reduction operation we consider, the intersection between both sets is either empty or a singleton containing the lexmax solution (Arin et al., 2003). This result induces a procedure for computing the lexmax solution for a class of games that contains games with large core (Sharkey,1982). We extend the previous analysis making use of the notion of anti-dual game (Oishi and Nakayama, 2009), finding parallel results for the lexmin solution. A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provide axiomatic characterizations by means of suitable properties such as consistency, rationality and Lorenz-fairness. As a by-product, alternative characterizations of the egalitarian solution over the class of convex games are obtained. Using the notion of anti-duality to axioms (Oishi et al. 2016), we obtain additional axiomatizations of the egalitarian solution on the domain of exact partition games but also on the domain of convex games. On the domain of balanced games, new axiomatic characterizations of the Lorenz maximal core are obtained. We introduce the Lorenz stable set and provide an axiomatic characterization in terms of constrained egalitarianism and projection consistency. On the domain of all coalitional games, we find that this solution connects the weak constrained egalitarian solution (Dutta and Ray, 1989) with their strong counterpart (Dutta and Ray, 1991).