New axiomatizations of values of TU-games using reduction properties

Andrzej Młodak¹

¹ Statistical Office in Poznań Branch in Kalisz Pl. J. Kilińskiego 13 62-800 Kalisz, Poland

Applicationes Mathematicae, Tome 40 (2013) no. 4, pp. 483-502

Résumé

We propose new axiomatizations of values of cooperative games where traditional properties connected with special players (dummy, null or zero) are replaced with weaker properties relating to such participants of the game. We assume that the change of payoff of a player when combining the game with another game where this player is special is constant. Using such axioms with an additional assumption that a value is odd and—if necessary—the fairness axioms holds, one can obtain axiomatizations without additivity where not only classical dummy, null or zero players axioms but even equal treatment can be redundant. These properties are used to construct new axiomatizations of the Shapley, Banzhaf and Deegan–Packel values. Some of them contain a new mirror game axiom.

Détail

DOI : 10.4064/am40-4-7

Keywords: propose axiomatizations values cooperative games where traditional properties connected special players dummy null zero replaced weaker properties relating participants game assume change payoff player combining game another game where player special constant using axioms additional assumption value odd necessary fairness axioms holds obtain axiomatizations without additivity where only classical dummy null zero players axioms even equal treatment redundant these properties construct axiomatizations shapley banzhaf deegan packel values contain mirror game axiom