Mechanism design for large scale systems.

In this paper, we consider infinite number of non atomic self-interested agents with private valuation of a divisible good. We design a pricing mechanism that is easy to implement, is individually rational, weakly budget balanced and incentive compatible. In this mechanism, agents send reports of their types, based on which, the designer solves a constrained optimization problem through Lagrange's mechanism. The resulting optimal allocation and Lagrange's multiplier is sent as the allocation and prices to the respective agent. We show that reporting one's type truthfully is a dominant strategy of the players in this mechanism. We then extend this idea to the dynamic case, when player's types are dynamically evolving as a controlled Markov process. In this case, in each time period, reporting one's type is a dominant strategy of the players.