NTU prenucleoli

Abstract

The prenucleolus for coalitional games with transferable utility (TU games) is a well established and intensively researched solution concept for this class of games. Unlike other solutions concepts for TU games (core, Shapley value, etc.) an extension to the class of all coalitional games without transferable utility (NTU games) must still be considered as an open problem. In this thesis we propose a new class of excess functions for NTU games and investigate the resulting prenucleoli for those games. These share some important properties with the TU prenucleolus like single-valuedness and the characterization by the Kohlberg criterion. A special member of this class of NTU prenucleoli is introduced which has some additional properties like covariance and consistency (with respect to a new reduced game, which is an extension of the Davis and Maschler reduced (TU) game). Also the connection to the core and a variant of it are investigated.