- Slides: 15
Communication Networks A Second Course Jean Walrand Department of EECS University of California at Berkeley
Yang-Hajek: VCG-Kelly Mechanism • • • Motivation Problem Mechanism Kelly’s Mechanism Problems with strategic players VCG Mechanism Hajek-Yang’s combination: VCG-Kelly Efficiency Stability Yank and Hajek: VCG-Kelly Mechanisms for Allocation of Divisible Goods: Adapting VCG Mechanisms to One-Dimensional Signals. 40 th Annual Conference on Information Sciences and Systems (CISS 06), Princeton, NJ, Mar 22 -24, 2006. .
Motivation • Problem: Efficient sharing of bandwidth in networks • Price-Taking Users: Kelly (One-dimensional bids) • Strategic Users: VCG (Infinite-dimensional bids: utility functions) • Combination: Efficient mechanism with onedimensional bids for strategic users
Problem (continued) Necessary and sufficient conditions
Kelly Mechanism Network problem Solution: User problem
Kelly Mechanism (continued) fi(x) = log(xi) surrogate valuation: Wi(x) = wilog(xi) one-dimensional signals: wi instead of Ui(x)
Problems with strategic players 1) NE may not exist for Kelly’s mechanism with strategic players: Necessary conditions for optimality imply x = (4, 1, 3), which is not an optimal point.
Problems with strategic players 1. 2) NE exists, it may be very inefficient: Social: x 0 = 0, xi = 1, I = 1, …, L NE: x 0 = g(g + L)-1, xi = (g + 1)-1 Loss: (g 2 + L)[L(g + 1)]-1 Let g 2 = L and let L
VCG Mechanism Incentive-Compatible: w() = u(. ) is dominant!
VCG Mechanism (continued) The bids are functions difficult to implement!
VCG-Kelly Mechanism (continued)
Efficiency Without fictitious bidders