On the Ordinal Invariance of Power Indices on Coalitional Games
Moretti, Stefano; Doignon, Jean-Paul; Ozturk, Meltem (2022), On the Ordinal Invariance of Power Indices on Coalitional Games, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI, p. 258-264. 10.24963/ijcai.2022/37
Type
Communication / ConférenceExternal document link
https://hal.archives-ouvertes.fr/hal-03829753Date
2022Conference title
Thirty-First International Joint Conference on Artificial Intelligence (IJCAI)Conference date
2022-07Conference city
VienneConference country
AustriaBook title
Proceedings of the Thirty-First International Joint Conference on Artificial IntelligencePublisher
IJCAI
ISBN
978-1-956792-00-3
Number of pages
5959Pages
258-264
Publication identifier
Metadata
Show full item recordAuthor(s)
Moretti, Stefano
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Doignon, Jean-Paul
Département de mathématiques Université Libre de Bruxelles
Ozturk, Meltem
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
In a coalitional game, the coalitions are weakly ordered according to their worths in the game. When moreover a power index is given, the players are ranked according to the real numbers they are assigned by the power index. If any game inducing the same ordering of the coalitions generates the same ranking of the players then, by definition, the game is (ordinally) stable for the power index, which in turn is ordinally invariant for the game. If one is interested in ranking players of a game which is stable, re-computing the power indices when the coalitional worths slightly fluctuate or are uncertain becomes useless. Bivalued games are easy examples of games stable for any power index which is linear. Among general games, we characterize those that are stable for a given linear index. Note that the Shapley and Banzhaf scores, frequently used in AI, are particular semivalues, and all semivalues are linear indices. To check whether a game is stable for a specific semivalue, it suffices to inspect the ordering of the coalitions and to perform some direct computation based on the semivalue parameters.Subjects / Keywords
Agent-based and Multi-agent Systems: Cooperative Games, Agent-based and Multi-agent Systems: Computational Social ChoiceRelated items
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