On the generalized dimension and codimension of simple games
| Autor: | Xavier Molinero, Fabián Riquelme, Salvador Roura, Maria Serna |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. Departament de Ciències de la Computació, Universitat Politècnica de Catalunya. ALBCOM - Algorísmia, Bioinformàtica, Complexitat i Mètodes Formals |
| Rok vydání: | 2023 |
| Předmět: |
Information Systems and Management
General Computer Science 91 Game theory economics social and behavioral sciences::91A Game theory [Classificació AMS] Management Science and Operations Research Industrial and Manufacturing Engineering Weighted voting games Codimension Modeling and Simulation Canonical minimum representation Vot -- Models matemàtics Voting -- Mathematical models Jocs Teoria de Dimension Matemàtiques i estadística::Investigació operativa::Teoria de jocs [Àrees temàtiques de la UPC] Game theory |
| Zdroj: | European Journal of Operational Research. 306:927-940 |
| ISSN: | 0377-2217 |
| Popis: | Weighted voting games are simple games that can be represented by a collection of integer weights for each player so that a coalition wins if the sum of the player weights matches or exceeds a given quota. It is known that a simple game can be expressed as the intersection or the union of weighted voting games. The dimension (codimension) of a simple game is the minimum number of weighted voting games such that their intersection (union) is the given game. In this work, we analyze some subclasses of weighted voting games and their closure under intersection or union. We introduce generalized notions of dimension and codimension regarding some subclasses of weighted voting games. In particular, we show that not all simple games can be expressed as intersection (union) of pure weighted voting games (those in which dummy players are not allowed) and we provide a characterization of such simple games. Finally, we experimentally study the generalized dimension (codimension) for some subclasses defined by establishing restrictions on the representations of weighted voting games |
| Databáze: | OpenAIRE |
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