Network Topology, Higher Orders of Stability and Efficiency

Stable networks of order r where r is a natural number refer to those networks that are immune to coalitional deviation of size r or less. In this paper, we introduce stability of a finite order and examine its relation with efficient networks under anonymous and component additive value functions and the component-wise egalitarian allocation rule. In particular, we examine shapes of networks or network architectures that would resolve the conflict between stability and efficiency in the sense that if stable networks assume those shapes they would be efficient and if efficient networks assume those shapes, they would be stable with minimal further restrictions on value functions.