Approximate Mechanism 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 Mechanism With money & Intractable Class 1 Opt SP Mechanism With money Intractable Class 2 No Opt SP Mechanism With Money Class 3 No 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

NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC UB 1 GSP rand 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 NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC LB open rand UB 2 GSP LB 2 SP det MC UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran Facility Location - Summary 7 Picture is from slides of [1]

Trees – Median is optimum 8 E E C C B B A A G G F F D D F F C C B B A A Picture is from slides of [1]

NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC LB open rand UB 2 GSP LB 2 SP det MC UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran Facility Location - Summary 9 Picture is from slides of [1]

Social Cost 10

NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC LB open rand UB 2 GSP LB 2 SP det MC UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran Facility Location - Summary 11 Picture is from slides of [1]

Maximum Cost 12 A A B B y y

NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC LB open rand UB 2 GSP LB 2 SP det MC UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran Facility Location - Summary 13 Picture is from slides of [1]

Maximum Cost – Randomized UB 14 E E D D A A C C 1/4 1/2 1/4 B B B B 1/2 d 2d Picture is from slides of [1]

NETWORK TOPOLOGY generalcircletreeline Mechanism Target LB  (n) SP UB 1 GSP det SC LB open rand UB 2 GSP LB 2 SP det MC UB 3/2 SP UB 3/2 GSP LB 3/2 SP ran 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 RndDet Single Matching

Single – Deterministic UB 19

Single – Randomized UB 20

Matching 21 C1 C n n OPT=3 OPT’=4

? 22 Thanks

Refrences 1.N. Alon, M. Feldman, A. D. Procaccia, M. Tennenholtz. Strategyproof Approximation Mechanisms for Location on Networks. CoRR, A. D. Procaccia, M. Tennenholtz. Approximate mechanism design without money. In Proceedings of the 10th ACM Conference on Electronic Commerce (ACM-EC), 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,

24 B B C C D D E E 1/4 F F 1/2 1/4 A A

25 B B 3/8 B B A A C C C C A A 1/4