Local requirements for optimal distribution of heterogeneous agents

This paper introduces an analytical framework for the study of a generic distribution problem where a group of heterogeneous agents intend to divide themselves into various subgroups without any form of global information-sharing or centralized decision-making. Subgroups are associated to mathematical functions that capture the marginal utilities of performing tasks, each satisfying the law of diminishing returns. We prove that under generic local requirements a stable agent distribution representing a Nash equilibrium can be achieved, and show via Monte Carlo simulations how the proposed set of rules performs under varying constraints on information flow and degrees of cooperation.