Three hierarchies of simple games parameterized by ‘resource’ parameters

Three hierarchies of simple games parameterized by ‘resource’ parameters

0.00 Avg rating0 Votes
Article ID: iaor20131237
Volume: 42
Issue: 1
Start Page Number: 1
End Page Number: 17
Publication Date: Feb 2013
Journal: International Journal of Game Theory
Authors: , ,
Keywords: competition and coalition
Abstract:

This paper contributes to the program of numerical characterization and classification of simple games outlined in the classic monograph of von Neumann and Morgenstern. We suggest three possible ways to classify simple games beyond the classes of weighted and roughly weighted games. To this end we introduce three hierarchies of games and prove some relationships between their classes. We prove that our hierarchies are true (i.e., infinite) hierarchies. In particular, they are strict in the sense that more of the key ‘resource’ (which may, for example, be the size or structure of the ‘tie‐breaking’ region where the weights of the different coalitions are considered so close that we are allowed to specify either winningness or nonwinningness of the coalition) yields the flexibility to capture strictly more games.

Reviews

Required fields are marked *. Your email address will not be published.