Effect of money heterogeneity on resource dependency in complex networks

Exchange of resources among individual components of a system is fundamental to systems like a social network of humans and a network of cities and villages. For various reasons, the human society has come up with the notion of \emph{money} as a proxy for the resources. Here we extend the model of resource dependencies in networks, proposed in [\href{https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.062304}{Phys. Rev. E {\bf 102}, 062304 (2020)}], by incorporating the notion of money so that the vertices of a network can sell and buy required resources among themselves. We simulate the model using the configuration model as a substrate for homogeneous as well as heterogeneous degree distributions and using various exchange strategies. We show that a moderate amount of initial heterogeneity in the money on the vertices can significantly improve the survivability of Scale-free networks but not that of homogeneous networks like the Erd{\H o}s-R{\'e}nyi network.