On the position value for communication situations with fuzzy coalition

Abstract

Borm et al. (1992) characterized the position value for cooperative games with deterministic communication structure introduced by Myerson (1977). Now we follow the Myerson model to consider the uncertainty about the participation levels of players. In this setting, the position value defined in terms of its crisp version is associated with partitions by levels of players and different ways to obtain these partitions lead to different position values with particular forms. We provide several characterizations of the specific position values from the perspective of generalized component efficiency and balanced link contributions, link potential function, and effort function linked to the Choquet partition and multilinear partition respectively.