Distributed and Cooperative Task Processing: Cournot Oligopolies on a Graph

This paper introduces a novel framework for the design of distributed agents that must complete externally generated tasks but also can volunteer to process tasks encountered by other agents. To reduce the computational and communication burden of coordination between agents to perfectly balance load around the network, the agents adjust their volunteering propensity asynchronously within a fictitious trading economy. This economy provides incentives for nontrivial levels of volunteering for remote tasks, and thus load is shared. Moreover, the combined effects of diminishing marginal returns and network topology lead to competitive equilibria that have task reallocations that are qualitatively similar to what is expected in a load-balancing system with explicit coordination between nodes. In the paper, topological and algorithmic conditions are given that ensure the existence and uniqueness of a competitive equilibrium. Additionally, a decentralized distributed gradient-ascent algorithm is given that is guaranteed to converge to this equilibrium while not causing any node to over-volunteer beyond its maximum task-processing rate. The framework is applied to an autonomous-air-vehicle example, and connections are drawn to classic studies of the evolution of cooperation in nature.