Minimal winning coalitions and orders of criticality
| Autor: | Stefano Moretti, Marco Dall'Aglio, Michele Aleandri, Vito Fragnelli |
|---|---|
| Přispěvatelé: | Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision (LAMSADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Axiomatic approach
Computer science MathematicsofComputing_GENERAL General Decision Sciences Dual game 0102 computer and information sciences Management Science and Operations Research 01 natural sciences Order of criticality Hitting set Cardinality 050602 political science & public administration Axiom [INFO.INFO-GT]Computer Science [cs]/Computer Science and Game Theory [cs.GT] 05 social sciences Rank (computer programming) hitting set dual game axiomatic approach ComputingMilieux_PERSONALCOMPUTING TheoryofComputation_GENERAL DUAL (cognitive architecture) Lexicographical order Blocking (computing) 0506 political science Ranking 010201 computation theory & mathematics Theory of computation Mathematical economics |
| Zdroj: | Annals of Operations Research Annals of Operations Research, Springer Verlag, 2021, ⟨10.1007/s10479-021-04199-6⟩ |
| ISSN: | 0254-5330 1572-9338 |
| DOI: | 10.1007/s10479-021-04199-6⟩ |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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