Optimal distribution of heterogeneous agents under delays

An analytical framework for the study of a generic distribution problem is introduced in which a group of agents with different capabilities intend to maximize total utility by dividing themselves into various subgroups without any form of global information-sharing or centralized decision-making. The marginal utility of belonging to a particular subgroup rests on the well-known concept in economic theory of the law of diminishing returns. For a class of discrete event systems, we identify a set of conditions that define local information and cooperation requirements, and prove that if the proposed conditions are satisfied a stable agent distribution representing a Pareto optimum is achieved even under random but bounded decision and transition delays.