Graph and Hypergraph Topologies in Decentralized Coalition Consensus Control for Financial and Economic Networks

Abstract

This work explores network coalition-based models using dynamic average consensus protocols, where agents in coalitions interact to reach global agreement. We employ hypergraphs to model communication structures and compare their convergence rates with clique expansion graphs. Our results show that hypergraph-based models achieve faster convergence for the case of continuous consensus dynamical systems and also in discrete time for coalitions with an equal number of agents. Our findings suggest that hypergraphs offer a scalable, decentralized approach to improving consensus algorithms in generalized tree like information structures, with significant potential for enhancing performance in applications like finance and economics.