Distributed Dynamics and Stable Outcomes in Coalitional Games and B-Matchings

Abstract Cooperative games model strategic settings in which agents coordinate to form partnerships and share payoffs to achieve mutually beneficial outcomes. These settings range from pairwise matchings to larger groups forming coalitions. In this paper, we address two setups of cooperative games: transferable utility coalitional games and bipartite B -matchings. For both settings, we propose distributed dynamics where agents form and break partnerships according to evolving internal aspiration levels that reflect self-interest. Our distributed dynamics require simple computations, limited memory, and minimal knowledge of the environment. We prove that these dynamics converge to stable outcomes analogous to the core, where no group of agents has an incentive to deviate from the proposed partnerships. We illustrate our dynamics through computational experiments on exchange networks. The simulations exhibit resilient behavior of the algorithms under message drops between the agents and dynamic entry and exit of agents.