Efficient MultiResource, MultiUnit VCG Auction
Abstract
We consider the optimization problem of a multiresource, multiunit VCG auction that produces an optimal, i.e., nonapproximated, social welfare. We present an algorithm that solves this optimization problem with pseudopolynomial complexity and demonstrate its efficiency via our implementation. Our implementation is efficient enough to be deployed in real systems to allocate computing resources in fine timegranularity. Our algorithm has a pseudonearlinear time complexity on average (over all possible realistic inputs) with respect to the number of clients and the number of possible unit allocations. In the worst case, it is quadratic with respect to the number of possible allocations. Our experiments validate our analysis and show nearlinear complexity. This is in contrast to the unbounded, nonpolynomial complexity of known solutions, which do not scale well for a large number of agents. For a single resource and concave valuations, our algorithm reproduces the results of a wellknown algorithm. It does so, however, without subjecting the valuations to any restrictions and supports a multiple resource auction, which improves the social welfare over a combination of singleresource auctions by a factor of 2.550. This makes our algorithm applicable to real clients in a real system.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.09014
 Bibcode:
 2019arXiv190509014F
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Data Structures and Algorithms
 EPrint:
 24 pages