Stability and Efficiency of Weighted Monoplex Networks: A Comparative Analysis with Multiplex Representation

This paper investigates stability conditions for weighted monoplex (single-layer) networks obtained by transformation of multiplex networks. We develop two comprehensive frameworks for such a transformation that take into account information including the length of the shortest path and the number of direct links between players in different layers to analyse network stability through utility functions depending on benefits and costs. Three different cost functions are investigated. The study establishes stability conditions for key network structures, including monoplex networks obtained by transforming all-layer complete, all-layer star (with identical or different centers), and unique-over-layers network configurations. Through comparative analysis, we examine when stability properties are preserved or altered when transforming multiplex networks into weighted monoplex networks.