Efficient coordinations of large-scale elastic loads with MCP and PSP auction mechanisms

In this paper, we propose a distributed method to coordinate large-scale elastic load units with auction mechanisms which have been widely applied in resource allocation problems. Distinct from the progressive second price (PSP) auction mechanism, under the market clearing price (MCP) auction mechanism, the incentive compatibility does not hold in general but holds with respect to the efficient bid profiles of other agents. We observe that the difference between the payments under PSP and MCP mechanisms vanishes as the population size goes to infinity and consequently show that the efficient bid strategy is an epsilon-Nash equilibrium in MCP auction games with epsilon converges to zero as the population size goes to infinity. As another key result developed in the paper we further show that the efficient bid strategy is an epsilon-Nash equilibrium of auction game systems with epsilon is on the second order of the second derivative of the generation cost which goes to zero as the population size goes to infinity in scalable systems.