Communication Networks

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Communication Networks

• A Second Course

Jean Walrand Department of EECS University of
California at Berkeley
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Yang-Hajek VCG-Kelly Mechanism

• Motivation
• Problem
• Mechanism
• Kellys Mechanism
• Problems with strategic players
• VCG Mechanism
• Hajek-Yangs 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.
.
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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

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Problem (continued)
Necessary and sufficient conditions
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Mechanism
bids
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Kelly Mechanism
? Network problem
Solution
? User problem
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Kelly Mechanism (continued)
fi(x) log(xi) ? surrogate valuation Wi(x)
wilog(xi) ? one-dimensional signals wi instead
of Ui(x)
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Problems with strategic players
1) NE may not exist for Kellys mechanism
with strategic players
Necessary conditions for optimality imply x
(4, 1, 3), which is not an optimal point.
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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 ? ?
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VCG Mechanism
Incentive-Compatible w() u(.) is dominant!
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VCG Mechanism (continued)
The bids are functions ? difficult to implement!
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VCG-Kelly Mechanism
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VCG-Kelly Mechanism (continued)
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Efficiency
Without fictitious bidders
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Stability