Distributed and Efficient Resource Balancing Among Many Suppliers and Consumers

Achieving a balance of supply and demand in a multi-agent system with many individual self-interested and rational agents that act as suppliers and consumers is a natural problem in a variety of real-life domains---smart power grids, data centers, and others. In this paper, we address the profit-maximization problem for a group of distributed supplier and consumer agents, with no inter-agent communication. We simulate a scenario of a market with $S$ suppliers and $C$ consumers such that at every instant, each supplier agent supplies a certain quantity and simultaneously, each consumer agent consumes a certain quantity. The information about the total amount supplied and consumed is only kept with the center. The proposed algorithm is a combination of the classical additive-increase multiplicative-decrease (AIMD) algorithm in conjunction with a probabilistic rule for the agents to respond to a capacity signal. This leads to a nonhomogeneous Markov chain and we show almost sure convergence of this chain to the social optimum, for our market of distributed supplier and consumer agents. Employing this AIMD-type algorithm, the center sends a feedback message to the agents in the supplier side if there is a scenario of excess supply, or to the consumer agents if there is excess consumption. Each agent has a concave utility function whose derivative tends to 0 when an optimum quantity is supplied/consumed. Hence when social convergence is reached, each agent supplies or consumes a quantity which leads to its individual maximum profit, without the need of any communication. So eventually, each agent supplies or consumes a quantity which leads to its individual maximum profit, without communicating with any other agents. Our simulations show the efficacy of this approach.