Some values for constant-sum and bilateral cooperative games

Andrzej M/lodak¹

¹ Central Statistical Office Statistical Office in Pozna/n Branch in Kalisz Pl. J. Kili/nskiego 13 62-800 Kalisz, Poland

Applicationes Mathematicae, Tome 34 (2007) no. 3, pp. 359-371

Résumé

We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of constant-sum or bilateral games, respectively. Moreover, a new axiomatization of the Deegan–Packel value on the set of all cooperative games is presented and possibilities of creation of its version in those special cases are discussed.

Détail

DOI : 10.4064/am34-3-7

Keywords: prove axiomatizations shapley value banzhaf value defined class nonnegative constant sum games nonzero worth grand coalition nonnegative bilateral games nonzero worth grand coalition characteristic feature latter class cooperative games game coalition its complement set players have worth axiomatizations generalized entire class constant sum bilateral games respectively moreover axiomatization deegan packel value set cooperative games presented possibilities creation its version those special cases discussed