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Quantized VCG Mechanisms for Polymatroid Environments
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
Application of Market Models to Network Equilibrium Problems
We present a general two-side market model with divisible commodities and
price functions of participants. A general existence result on unbounded sets
is obtained from its variational inequality re-formulation. We describe an
extension of the network flow equilibrium problem with elastic demands and a
new equilibrium type model for resource allocation problems in wireless
communication networks, which appear to be particular cases of the general
market model. This enables us to obtain new existence results for these models
as some adjustments of that for the market model. Under certain additional
conditions the general market model can be reduced to a decomposable
optimization problem where the goal function is the sum of two functions and
one of them is convex separable, whereas the feasible set is the corresponding
Cartesian product. We discuss some versions of the partial linearization
method, which can be applied to these network equilibrium problems.Comment: 18 pages, 3 table
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