VCG Auction Mechanism Cost Expectations and Variances.
arXiv: Computer Science and Game Theory(2013)
摘要
We consider Vickrey-Clarke-Groves (VCG) auctions for a very general combinatorial structure, in an average-case setting where item costs are independent, identically distributed uniform random variables. We prove that the expected VCG cost is at least double the expected nominal cost, and exactly double when the desired structure is a basis of a bridgeless matroid. In the matroid case we further show that, conditioned upon the VCG cost, the expectation of the nominal cost is exactly half the VCG cost, and we show several results on variances and covariances among the nominal cost, the VCG cost, and related quantities. As an application, we find the asymptotic variance of the VCG cost of the minimum spanning tree in a complete graph with random edge costs.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络