ApproximateMechanism Design

Without Money

App. Mech. Design Without Money

• Mechanism

• Truthfulness

• Without money

2

VCG

Money is the root of all evil!

• Security issues

• Banking issues

• Ethical Considerations

• Legal Considerations

3

App. Mech. Design Without Money

• Mechanism

• Truthfulness

• Without money

• Approximation

4

VCG

Problem Classes

5

Opt Sp MechanismWith money

&Intractable

Class 1Opt SP Mechanism

With moneyIntractable

Class 2No Opt SP

Mechanism With Money

Class 3No opt SP Mechanism

Without Money

Picture is from slides of [1]

Facility Location - Definitions

• Network, Graph

• Agents

• Location Profile

• Deterministic Mechanism

• Randomized Mechanism

• SP and GSP

6

Facility Location - Summary

7

Picture is from slides of [1]

Trees – Median is optimum

8

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GG

FF

DD

FF

CC

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AA

Picture is from slides of [1]

Facility Location - Summary

9

Picture is from slides of [1]

Social Cost

10

Facility Location - Summary

11

Picture is from slides of [1]

Maximum Cost

12

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Facility Location - Summary

13

Picture is from slides of [1]

Maximum Cost – Randomized UB

14

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Picture is from slides of [1]

Facility Location - Summary

15

Picture is from slides of [1]

Election - Definitions

• Voters

• Candidates

• Preference List

• Preference Profile

• Approximation

16

Single

• Mechanism

• Benefit

Election – Definitions (cont.)

17

Matching

• Mechanism

• Benefit

Election - Summary

18

Single – Deterministic UB

19

Single – Randomized UB

20

Matching

21

C1C1 C2C2

11 22 33 nn

1

1 2 22

1

2

1

OPT=3

OPT’=4

?22

ThanksThanks

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.

23

24

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25

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