20130527 mechanism design

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<ul><li> 1. (oono@preferred.jp)2013/5/27PPDM@</li></ul> <p> 2. Mechanism Collusion Resistance Differential Privacy Truthfulness Optimal Mechanism3 Unlimited Supply Auction Attribute Auction Constrained Pricing Problem 3. [1] bidder/auctioner utility function/collusion 1.1 4. [1]12 16 1812152015151530 0 1 3 Mechanism 5. 6. [1] 7. Truthfulness =Truthful Utility Function Truthfulness Bayes-Nash equilibrium/strongly truthful with high probability/undominated strategy in for single-value combinatorialauction/example in shortest path auction/-Nash/myopicequilibrium/-dominant strategy implementation 8. b1 bi bnd1didnrrrbi(r)bn(r)bib1(r)q(D, r)r=M(D)M, qM:()q:()D=(d1, .., dn):B=(b1, .., bn):E[q(D, r)] 9. -Differential PrivacyMechanism Mechanism-Differential PrivacyD1D2MM 10. Truthfulness or Truthful Truth telling or -Approximate truthful (1+)Truthful 11. Dominant Strategy SDominant Strategy S Cf. S-Dominant Strategy S(1+)Dominant Strategy 12. -Differential PrivacyMechanism1approximate truthfulness -Differential Privacy-approximatetruthful Truth telling(exp()-1)-dominantstrategy Lemma3Lemma3g2 by definition 13. -Differential PrivacyMechanism2Collusion Resistance Truthfulapproximate truthful 14. -Differential PrivacyMechanism3Composability Differential PrivacyMechanismMechanismDifferential Privacy 15. Mechanism DifferentialPrivacyThm 6 Theorem 8 Lemma7 dDiff. Privacy dr q: qgiven q R 16. Differential PrivacyTheorem 6 qq Differential Privacy q=Diff. Privacy 1distributionexp(q)!q := maxisupr,Ddisupdiq(D,r)" infdiq(D,r)#$%&amp;( 17. Theorem 8a OPT=supr q(d, r) given dsupglobaloptimal 18. general 1Unlimited Supply Auction 2Attribute Auction 3Constrained Pricing Problems 19. 1Unlimited Supply Auction 0 Demand curve bi : [0, 1]R ([0, 1]) bi(p) = ip bi bqq(d, p)=pbi(p) 0= q=1Eq2-Diff Privacy Thm. 9 20. Unlimited Supply AuctionThm.9 Notation OPT=supp q(d, p) pOPT=argmaxp q(d, p) m=OPT/pOPTbi(pOPT) [0, 1]Thm.8tlog(e+2OPT m)/ 21. 2Attribute Auction nk kSegmentnkSEG_{k} Unlimited supply auctionBasemasure Segmentk Segmentk Segment1nn 22. 3Constrained Pricing Problem kGoods1 1 Unlimited supply auctionextension Unlimited supply auctionR=[0, 1]R=[k]x[0, 1] 23. Discussion/Future Work biq qpiecewise linear output space OPT=maxr q (d, r) Differential Privacymechanism design 24. Differential Privacy q Approximate Truthfulness Differential Privacy Collusion Resistance q q3 1Unlimited Supply Auction 2Attribute Auction 3Constrained Pricing Problems 25. [1], 1599 2008 189-194 26. </p>