1. (Algorithmic) Mechanism Design Paolo Penna

2. Mechanism Design Find correct rules/incentives

3. Not in this talk Mechanisms without money (voting) Fish Meat Vegetarian Coordination mechanisms This talk

4. Example: BGP AS1 AS2 source destination Congestion

5. A Toy Problem sd 2 10 100 private costs

6. A Toy Problem sd 2 10 Payments: declared cost 9.999

7. A Toy Problem sd 2 10 Payments: 2 nd best cost 9.999 utility(“truth”) = 10 – 2 ≥ utility(“false”) Truthful Mechanism

8. VCG Mechanisms Algorithm: Minimize the sum of all costs SP, MST, Steiner Tree, … Payments: opt 2 nd best sol Truthful Mechanism (Vickerey'61 – Clarke'71 – Groves'73)

9. VCG Mechanisms Algorithm: Minimize the sum of all costs SP, MST, Steiner Tree, … Payments: opt 2 nd best sol Truthful Mechanism (Vickerey'61 – Clarke'71 – Groves'73) NP-hard Min-Max?

10. Other Mechanisms? Players CostsGlobal Costs any sum All truthful mechanisms are VCG (Roberts'79) “simpler” “more” Other mechanisms exist (Myerson'81,..., Saks&Yu'05,...)

11. Mechanism Design ≡ Algorithm Design sd t1t1 t2t2 selected i titi work i sd t1t1 t2t2 titi... any problem suitable inequality Truthful mechanism (A, P) Monotone algorithm A (Myerson'81,...,Bikhchandani et al'06, Saks&Yu'05,...)

12. Monotone Algorithms? work i sd 3 2 2 t1t1 titi t2t2 3 2 2 2 2 3 1+ ℇ 1 Greedy: 1+ ℇ 1 (1+ ℇ ) 2 not monotone

13. Monotone Algorithms? work i sd 3 2 2 t1t1 titi t2t2 Redesign approximation algorithms: PTAS or FPTAS still possible for related machines (...,Andelman et al'07, Christodoulou&Kovacs'10)

14. Monotonicity Truthful mechanism (A, P) Monotone algorithm A No monotone c-APX algorithm Yes monotone c-APX algorithm Unrelated machines: truthful APX is between 2 and m (Nisan&Ronen'99) Conjecture: m Complexity is not an issue (PTAS)

15. Problem Classification on/off one-parametermulti-parameterarbitrary sum, min-max, max-min... sum (VCG) only this (Roberts') VCG with polytime algos (Nisan&Ronen'00): Can be arbitrarily bad Feasibly-truthful (hard for mechanism ⇔ hard to cheat)

16. Problem Classification on/off one-parametermulti-parameterarbitrary sum, min-max, max-min... sum (VCG) only this (Roberts') Polytime or truthful alone is possible, but not both together (Papadimitriou&Schapira&Singer'08)

17. Problem Classification on/off one-parametermulti-parameterarbitrary sum, min-max, max-min... sum (VCG) only this (Roberts') False-identities can manipulate VCG (Yokoo&Sakurai&Matsubara'04)

18. Even more problems: 1) Collusion 2) Budget

19. Collusion sd 2 10 1000 No “useful” mechanism is collusion-resistant (Schummer'00) Payments: 2 nd best

20. Budget sd 2 10000 Payments: 2 nd best

21. Budget s d 1 v1v2 Global cost: C(S) – v1(S) - v2(S) Algorithm: min Global cost 2 nd best sol Payments: opt No budget, no collusion-resistant

22. Cost-sharing Users S service C(S) max Valuations - C(S) VCG Budget-balance Moulin'99 Mutually exclusive (...,Feigenbaum et al'03) Collusions

23. Cost-sharing Users S service C(S) First the payments ∑ i P(S,i) = C(S) P(S,i) Algorithm: offer prices...until all accept User s S1S1 S0S0 S2S2... Moulin

24. Cost-sharing Users S service C(S) Monotone payments ⇒ truthful P(S,i) S1S1 S0S0 S2S2... Moulin ≥ ≥

25. Similarities AS1 AS2 source destination Real BGP: Moulin: S1S1 S0S0 S2S2... Repeated Best-response Repeated Best-response BGP converges, collusion-proof, “budget-balance” (...,Gao&Rexford'01,...,Sami&Schapira&Zohar'09,...)

26. Unifying Theory Repeated Best Response on “nice” Game Converge + Incentive Compatible (Nisan&Schapira&Valiant&Zohar'11) Moulin,... BGP TCP Games Stable Matching

27. Unifying Theory Repeated Best Response on “nice” Game Converge + Incentive Compatible (Nisan&Schapira&Valiant&Zohar'11) Moulin,... BGP TCP Games Stable Matching

28. Unifying Theory Converge + Incentive Compatible (Nisan&Schapira&Valiant&Zohar'11) Moulin,... BGP TCP Games Stable Matching

29. Thank You