Before revision:  In this mechanism, agentssend 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.
After revision:  In this mechanism, agentssend reports of their types are their dominant strategies; for the finite case, each agent's incentive to misreport converges quadratically to zero. For practical implementation, we introduce a modified mechanism that possesses an additional important technical property, superimposability, which makes it able to be built upon any (potentially distributed) algorithm that optimally solves the NUM Problem and ensures all agents to obey the algorithm. We then extend this idea to the dynamic case, when player' s types are dynamically evolving as a controlled Markov process.