# Quantized VCG Mechanisms for Polymatroid Environments

## TL;DR

This paper introduces a quantized VCG mechanism for polymatroid environments that reduces communication costs by quantizing allocations and bids, while analyzing the trade-offs in efficiency and incentive compatibility.

## Contribution

It proposes a novel quantization approach for VCG mechanisms in polymatroid settings, maintaining incentive properties with lower communication requirements.

## Key findings

- Quantization reduces communication costs significantly.
- Efficiency loss due to quantization is characterized.
- Mechanism preserves dominant strategy incentive compatibility.

## Abstract

Many network resource allocation problems can be viewed as allocating a divisible resource, where the allocations are constrained to lie in a polymatroid. We consider market-based mechanisms for such problems. Though the Vickrey-Clarke-Groves (VCG) mechanism can provide the efficient allocation with strong incentive properties (namely dominant strategy incentive compatibility), its well-known high communication requirements can prevent it from being used. There have been a number of approaches for reducing the communication costs of VCG by weakening its incentive properties. Here, instead we take a different approach of reducing communication costs via quantization while maintaining VCG's dominant strategy incentive properties. The cost for this approach is a loss in efficiency which we characterize. We first consider quantizing the resource allocations so that agents need only submit a finite number of bids instead of full utility function. We subsequently consider quantizing the agent's bids.