Some values for constant-sum and bilateral cooperative games

Tom 34 / 2007

Andrzej M/lodak Applicationes Mathematicae 34 (2007), 359-371 MSC: Primary 91A12. DOI: 10.4064/am34-3-7

Streszczenie

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.

Autorzy

  • Andrzej M/lodakCentral Statistical Office
    Statistical Office in Pozna/n
    Branch in Kalisz
    Pl. J. Kili/nskiego 13
    62-800 Kalisz, Poland
    e-mail

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