In this paper, we consider infinite number of non atomic self-interested agentswith 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, 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. In this case, in each time period, reporting one's type is a dominant strategy of the players .
Network utility maximization (NUM) is a general framework for designing distributed optimization algorithms for large-scale networks. An economic challenge arises in the presence of strategic agents' private information. Existing studies proposed (economic) mechanisms but largely neglected the issue of large-scale implementation. Specifically, they require certain modifications to the deployed algorithms, which may bring the significant cost. To tackle this challenge, we present the large-scale Vickery-Clark-Grove (VCG) Mechanism for NUM, with a simpler payment rule characterized by the shadow prices. The Large-Scale VCG Mechanism maximizes the network utility and achieves individual rationality and budget balance. With infinitely many agents, agents' truthful 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 agents' types are dynamically evolving as a controlled Markov process. In this case, the mechanism leads to incentive compatible actions of agent for each time slot .
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In this paper, we consider infinite number of non atomic self-interested agentswith 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, agentssend
Network utility maximization (NUM) is a general framework for designing distributed optimization algorithms for large-scale networks. An economic challenge arises in the presence of strategic agents' private information. Existing studies proposed (economic) mechanisms but largely neglected the issue of large-scale implementation. Specifically, they require certain modifications to the deployed algorithms, which may bring the significant cost. To tackle this challenge, we present the large-scale Vickery-Clark-Grove (VCG) Mechanism for NUM, with a simpler payment rule characterized by the shadow prices. The Large-Scale VCG Mechanism maximizes the network utility and achieves individual rationality and budget balance. With infinitely many agents, agents' truthful
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, 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
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
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in each time period, reporting one's type is a dominant strategy of the players
the mechanism leads to incentive compatible actions of agent for each time slot