Decentralized Cooperative Network Games in Economics and Finance

Abstract

This paper introduces a new class of cooperative graphical games, where multiple coalitions engage in decentralized bargaining processes to optimize their collective goals. Unlike traditional cooperative game theory, which often overlooks the dynamics of internal bargaining within coalitions, our approach incorporates a graphical communication structure that includes multigraphs and hypergraphs. This framework introduces a novel concept, the “importance value,” which quantifies the influence of agents and coalitions in the bargaining process. By leveraging distributed optimization techniques, we employ a dual decomposition algorithm that guarantees convergence in a single iteration of bargaining. Additionally, combinatorial methods are used to determine the optimal allocation of agents to bargaining relationships, ensuring an efficient solution to the distributed optimization problem.