Approximate
Mechanism Design
Without Money
App. Mech. Design Without Money
• Mechanism
• Truthfulness
VCG
• Without money
2
Money is the root of all evil!
• Security issues
• Banking issues
• Ethical Considerations
• Legal Considerations
3
App. Mech. Design Without Money
• Mechanism
• Truthfulness
VCG
• Without money
• Approximation
4
Problem Classes
Class 1
Opt SP Mechanism
With money
Intractable
Opt Sp
Mechanism
With money
&
Intractable
Class 3
Class 2
Picture is from
slides of [1]
No Opt SP
Mechanism
With Money
No opt SP Mechanism
Without Money
5
Facility Location - Definitions
• Network, Graph
• Agents
• Location Profile
• Deterministic Mechanism
• Randomized Mechanism
• SP and GSP
6
Facility Location - Summary
NETWORK TOPOLOGY
Target
SC
Mechanism
line
tree
det
UB 1 GSP
UB 1 GSP
UB 1 GSP
UB 1 GSP
rand
det
MC
ran
circle
general
LB (n) SP LB (n) SP
LB open
UB 2 GSP
LB 2 SP
UB 3/2 GSP
LB 3/2 SP
UB 2 GSP
LB 2 SP
UB 2 GSP
LB 2 SP
UB 2 GSP
LB 2 SP
UB 3/2 SP
LB 3/2 SP
UB 2 GSP
LB 2-o(1) SP
Picture is from slides of [1]
7
Trees – Median is optimum
A
B
D
F
C
G
E
Picture is from slides of [1]
8
Facility Location - Summary
NETWORK TOPOLOGY
Target
Mechanism
line
det
SC
rand
det
MC
ran
tree
circle
UB 1 GSP
LB (n) SP
general
LB open
UB 2 GSP
LB 2 SP
UB 3/2 GSP
UB 3/2 SP
LB 3/2 SP
Picture is from slides of [1]
9
Social Cost
10
Facility Location - Summary
NETWORK TOPOLOGY
Target
Mechanism
line
det
SC
rand
det
MC
ran
tree
circle
UB 1 GSP
LB (n) SP
general
LB open
UB 2 GSP
LB 2 SP
UB 3/2 GSP
UB 3/2 SP
LB 3/2 SP
Picture is from slides of [1]
11
Maximum Cost
A
y
B
12
Facility Location - Summary
NETWORK TOPOLOGY
Target
Mechanism
line
det
SC
rand
det
MC
ran
tree
circle
UB 1 GSP
LB (n) SP
general
LB open
UB 2 GSP
LB 2 SP
UB 3/2 GSP
UB 3/2 SP
LB 3/2 SP
Picture is from slides of [1]
13
Maximum Cost – Randomized UB
d
2d
B
A
1/4
1/4
C
1/2
1/2
D
E
1/4
Picture is from slides of [1]
14
Facility Location - Summary
NETWORK TOPOLOGY
Target
Mechanism
line
det
SC
rand
det
MC
ran
tree
circle
UB 1 GSP
LB (n) SP
general
LB open
UB 2 GSP
LB 2 SP
UB 3/2 GSP
UB 3/2 SP
LB 3/2 SP
Picture is from slides of [1]
15
Election - Definitions
• Voters
• Candidates
• Preference List
• Preference Profile
• Approximation
16
Election – Definitions (cont.)
Single
Matching
• Mechanism
• Mechanism
• Benefit
• Benefit
17
Election - Summary
Det
Rnd
Single
Matching
18
Single – Deterministic UB
19
Single – Randomized UB
20
Matching
C1
C2
OPT=3
1
1
2
2
2
2
1
1
OPT’=4
1
2
3
n
21
?
Thanks
22
Refrences
1.
2.
3.
N. Alon, M. Feldman, A. D. Procaccia, M. Tennenholtz. Strategyproof
Approximation Mechanisms for Location on Networks. CoRR, 2009
A. D. Procaccia, M. Tennenholtz. Approximate mechanism design
without money. In Proceedings of the 10th ACM Conference on
Electronic Commerce (ACM-EC), 2009
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.
23
1/4
A
B
C
F
E
D
1/2
1/4
24
B
1/4
A
3/8
C
C
A
B
3/8
25