An average lexicographic value for cooperative games

• Published in: European journal of operational research 2011-08, Vol.213 (1), p.210-220
• Main Authors: Tijs, Stef, Borm, Peter, Lohmann, Edwin, Quant, Marieke
• Format: Article
• Language: English
• Subjects: Alexia value; Applied sciences; Big boss and clan games; Bosses; Compromise stability; Convexity; Dictionaries; Exact sciences and technology; Game theory; Game theory Alexia value Convexity Compromise stability Big boss and clan games; Games; Maxima; Minima; Operational research; Operational research and scientific management; Operational research. Management science; Studies
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.03.025

► The Alexia value is a new allocation rule for cooperative games. ► The Alexia value combines attractive properties of the Shapley value and the nucleolus. ► For convex games the Alexia value and the Shapley value coincide. ► For subclasses of compromise stable games an expression for the Alexia value is derived. For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.