Quantized Dominant Strategy Mechanisms with Constrained Marginal Valuations

We address the problem of designing efficient allocation mechanisms for a divisible resource, which is a fundamental problem in many networked systems. One milestone in mechanism design is the well-known Vickrey-Clarke-Groves (VCG) mechanism, where there exists a strictly dominant strategy for each agent. However, VCG mechanisms can require an excessive amount of communication making it impractical in some large networked systems. Alternative approaches have been studied that relax the incentive properties of VCG to limit communication. Alternatively, in prior work we considered the use of quantization as a way to reduce communication and maintain dominant strategy incentive compatibility, albeit with a loss of efficiency. Our prior work bounded this efficiency loss allowing for arbitrary concave increasing agent utilities. In this paper, we first refine this analysis when bounds on the marginal utility of an agent are known. In addition to quantizing the resource, we also study mechanisms that quantize the bids an agent can submit and again bound the overall efficiency loss given constraints on the agent's marginal valuations.