In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

Minimal winning coalitions and orders of criticality / Aleandri, Michele; Dall'Aglio, Marco; Fragnelli, V.; Moretti, S.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (In corso di stampa), pp. 1-17. [10.1007/s10479-021-04199-6]

Minimal winning coalitions and orders of criticality

Aleandri M.
Membro del Collaboration Group
;
Dall'Aglio M.
Membro del Collaboration Group
;
In corso di stampa

Abstract

In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.
Axiomatic approach; Dual game; Order of criticality; Hitting set
Minimal winning coalitions and orders of criticality / Aleandri, Michele; Dall'Aglio, Marco; Fragnelli, V.; Moretti, S.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (In corso di stampa), pp. 1-17. [10.1007/s10479-021-04199-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/209686
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