Axiomatization of values of cooperative games using a fairness property

Andrzej M/lodak¹

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

Applicationes Mathematicae, Tome 32 (2005) no. 1, pp. 69-86.

Résumé

We propose new systems of axioms which characterize four types of values of cooperative games: the Banzhaf value, the Deegan–Packel value, the least square prenucleolus and the least square nucleolus. The common element used in these axiomatizations is a fairness property. It requires that if to a cooperative game we add another game in which two given players are symmetric, then their payoffs change by the same amount. In our analysis we will use an idea applied by R. van den Brink (2001) to obtain an axiomatic characterization of the Shapley value.

Détail

DOI : 10.4064/am32-1-6

Keywords: propose systems axioms which characterize types values cooperative games banzhaf value deegan packel value least square prenucleolus least square nucleolus common element these axiomatizations fairness property requires cooperative game another game which given players symmetric their payoffs change amount analysis idea applied van den brink obtain axiomatic characterization shapley value