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Communication Networks

Explore VCG-Kelly mechanisms for sharing bandwidth in networks, addressing challenges with strategic users and optimizing efficiency. Learn about Kelly's and VCG mechanisms, their adaptations, and the importance of stability in allocation.

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Communication Networks

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  1. Communication Networks A Second Course Jean Walrand Department of EECS University of California at Berkeley

  2. 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. 40th Annual Conference on Information Sciences and Systems (CISS06), Princeton, NJ, Mar 22-24, 2006..

  3. 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 one-dimensional bids for strategic users

  4. Problem (continued) Necessary and sufficient conditions

  5. Mechanism “bids”

  6. Kelly Mechanism  Network problem Solution:  User problem

  7. Kelly Mechanism (continued) fi(x) = log(xi)  surrogate valuation: Wi(x) = wilog(xi)  one-dimensional signals: wi instead of Ui(x)

  8. 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.

  9. Problems with strategic players 2) NE exists, it may be very inefficient: Social: x0 = 0, xi = 1, I = 1, …, L NE: x0 = g(g + L)-1, xi = (g + 1)-1 Loss: (g2 + L)[L(g + 1)]-1Let g2 = L and let L  

  10. VCG Mechanism Incentive-Compatible: w() = u(.) is dominant!

  11. VCG Mechanism (continued) The bids are functions  difficult to implement!

  12. VCG-Kelly Mechanism

  13. VCG-Kelly Mechanism (continued)

  14. Efficiency Without fictitious bidders

  15. Stability

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