We use the axiomatization of the position value for network situations in van den Nouweland and Slikker (2012) to define a position value for partition function form network situations. We do this by generalizing the axioms to the partition function form value function setting as studied in Navarro (2007) and then showing that there exists a unique allocation rule satisfying these axioms. We call this allocation rule the position value for partition function form network situations.
Nouweland, van den, C. G. A. M., & Slikker, M. (2016). The position value for partition function form network games. Journal of Public Economic Theory, 18(2), 226-247. https://doi.org/10.1111/jpet.12138