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.