Lexicographical Maxmin Core Solutions for Cooperative Games

Abstract

Some cooperative game solutions can be represented with the help of functions measuring a distance between an arbitrary characteristic function (a characteristic function of a cooperative game) and an additive function defined on the players’ power set. In contrast to such ‘utilitarian’ solutions there are ‘egalitarian’ ones minimizing the maximal difference between the values of these functions, and their lexicographic extensions.In this paper we use such an approach to cooperative games with or without transferable utilities (TU and NTU) and with non-empty cores. A new egalitarian solution called a lexicographical maxmin core solution (LMCS) is defined. It assigns to each cooperative game the payoff vector defined by the lexicographic maximization of minimal components of the vectors from the core. Axiomatization of the LMCS, both for TU and NTU games, is given. It turns out that for convex TU games, the LMCS coincides with the Dutta egalitarian solution.KeywordsCooperative game(non)transferable utilitiescooperative game solutionaxiomatic characterizationleximin preference relation