Approximate Mechanism Design Without Money

1
ApproximateMechanism Design Without Money
2
App. Mech. Design Without Money

• Mechanism
• Truthfulness
• Without money

VCG
3
Money is the root of all evil!

• Security issues
• Banking issues
• Ethical Considerations
• Legal Considerations

4
App. Mech. Design Without Money

• Mechanism
• Truthfulness
• Without money
• Approximation

VCG
Facility Location
Election
5
Problem Classes
Class 1 Opt SP Mechanism With money Intractable
Opt Sp Mechanism With money Intractable
Class 3 No opt SP Mechanism Without Money
Class 2 No Opt SP Mechanism With Money
Picture is from slides of 1
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Facility Location - Definitions

• Network, Graph
• Agents
• Location Profile
• Deterministic Mechanism
• Randomized Mechanism
• SP and GSP

 
 
 
 
 
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Facility Location - Summary
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP LB ?(n) SP UB 1 GSP UB 1 GSP det SC
UB 1 GSP UB 1 GSP rand SC
UB 2 GSP LB 2 SP UB 2 GSP LB 2 SP UB 2 GSP LB 2 SP UB 2 GSP LB 2 SP det MC
UB 2 GSP LB 2-o(1) SP UB 3/2 SP LB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP UB 1 GSP det SC
LB open rand SC
UB 2 GSP LB 2 SP det MC
UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
Picture is from slides of 1
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Trees Median is optimum
A
A
B
B
D
F
F
C
C
G
E
Picture is from slides of 1
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Facility Location - Summary
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP UB 1 GSP det SC
LB open rand SC
UB 2 GSP LB 2 SP det MC
UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
Picture is from slides of 1
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Social Cost

•  

 
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Facility Location - Summary
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP UB 1 GSP det SC
LB open rand SC
UB 2 GSP LB 2 SP det MC
UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
Picture is from slides of 1
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Maximum Cost

•  

A
y
B
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Facility Location - Summary
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP UB 1 GSP det SC
LB open rand SC
UB 2 GSP LB 2 SP det MC
UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
Picture is from slides of 1
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Maximum Cost Randomized UB

•  

 
d
2d
A
C
B
B
E
D
1/4
1/2
1/2
1/4
1/4
Picture is from slides of 1
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Facility Location - Summary
NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY NETWORK TOPOLOGY
general circle tree line Mechanism Target
LB ?(n) SP UB 1 GSP det SC
LB open rand SC
UB 2 GSP LB 2 SP det MC
UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran MC
Picture is from slides of 1
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Election - Definitions

• Voters
• Candidates
• Preference List
• Preference Profile
• Approximation

 
 
 
 
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Election Definitions (cont.)

• Matching
• Mechanism
• Benefit

• Single
• Mechanism
• Benefit

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Election - Summary
Rnd Det
Single
Matching
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Single Deterministic UB

•  

 
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Single Randomized UB

•  

 
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Matching

•  

C1
C2
2
OPT3
1
OPT4
1
2
3
n
22

• ?

Thanks
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Refrences

1. N. Alon, M. Feldman, A. D. Procaccia, M.
   Tennenholtz. Strategyproof Approximation
   Mechanisms for Location on Networks. CoRR, 2009
2. A. D. Procaccia, M. Tennenholtz. Approximate
   mechanism design without money. In Proceedings of
   the 10th ACM Conference on Electronic Commerce
   (ACM-EC), 2009
3. J. Schummer and R. V. Vohra. Mechanism design
   without money. In N. Nisan, T. Roughgarden, E.
   Tardos, and V. Vazirani, editors, Algorithmic
   Game Theory, chapter 10. Cambridge University
   Press, 2007.

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1/4
A
B
C
F
D
1/2
E
1/4
25
B
1/4
A
3/8
C
C
A
B
3/8