Abstract
In this paper we give structural characterizations of disjunctive and conjunctive hierarchical simple games by characterizing them as complete games with a unique shift-maximal losing coalition, and a unique shift-minimal winning coalition, respectively. We prove canonical representation theorems for both types of hierarchical games and establish duality between them. We characterize the disjunctive and conjunctive hierarchical games that are weighted majority games. This paper was inspired by Beimel et al. (2008) and Farràs and Padró (2010) characterizations of ideal weighted threshold access structures of secret sharing schemes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
