Strong Implementation of Social Choice Functions in Dominant Strategies - PowerPoint PPT Presentation

harper
strong implementation of social choice functions in dominant strategies n.
Skip this Video
Loading SlideShow in 5 Seconds..
Strong Implementation of Social Choice Functions in Dominant Strategies PowerPoint Presentation
Download Presentation
Strong Implementation of Social Choice Functions in Dominant Strategies

play fullscreen
1 / 27
Download Presentation
Strong Implementation of Social Choice Functions in Dominant Strategies
75 Views
Download Presentation

Strong Implementation of Social Choice Functions in Dominant Strategies

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Strong Implementation of Social Choice Functions in Dominant Strategies Clemens ThielenSven O. Krumke 3rd International Workshop on ComputationalSocial Choice 15 September 2010 krumke@mathematik.uni-kl.de TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA

  2. Problem Definition • Social choice setting with private information: Strong Implementability

  3. Mechanisms Mechanism: Types Bids Social Choices Agent 1 strategy α1 . . . g strategy αn Agent n . . . Strong Implementability

  4. Utilities andEquilibria Definition: valuationoftheoutput paymentobtained Strong Implementability

  5. Utilities andEquilibria Definition: Definition: Strong Implementability

  6. Strong Implementation Definition: Strong Implementability

  7. Strong Implementability Problem The Strong Implementability Problem: Encoding length: Strong Implementability

  8. Augmented Revelation Mechanisms Definition: Augmented Revelation Principle: [Mookherjee, Reichelstein 1990] „incentivecompatibility“ Strong Implementability

  9. PreviousResults Strong Implementability

  10. Previous Results (2) Strong Implementability

  11. OurResults Strong Implementability

  12. Augmented Revelation Principle Augmented Revelation Principle: [Mookherjee, Reichelstein 1990] Augmented Revelation Principlefor Dominant Strategies: [thispaper] Strong Implementability

  13. General Idea (I) • To obtain an augmented revelation mechanism: seedefinitiontofollowsoon Definition: Strong Implementability

  14. Selective Elimination agenti Strong Implementability

  15. Selective Elimination Strong Implementability

  16. Bad Pairs and Elimination Definition: Definition: Definition: Strong Implementability

  17. TwoImportantSteps Theorem 2 (selectiveeliminationisnecessary): Theorem 3 (selectiveeliminationissufficient): Strong Implementability

  18. StructureoftheAlgorithm Theorem 3 + closelookattheproof guess Definitionofselectiveelimination guess verify Strong Implementability

  19. The Verification General Approach: Main Observation: Strong Implementability

  20. The Payment Polyhedron Strong Implementability

  21. The Payment Polyhedron (I) Incentivecompatibility & dominant bids Inequalitiesencodewhichbidsare dominant bids. Strong Implementability

  22. The Payment Polyhedron (II) Inequalitiesencodeconditionsofselectiveelimination Strong Implementability

  23. The Payment Polyhedron (II) Inequalitiesencodeconditionsofselectiveelimination Strong Implementability

  24. VerificationIssues Here I am! Strong Implementability

  25. VerificationIssues Wehaveto handle strictinequalities. To do so, we must find a point in therelative interiorofthepolyhedron. Thiscanbedonebymeansofthe Ellipsoid Method (directly) orbysolving a sequenceof LPs. Byproduct: Paymentsareofpolynomialencodinglength. Strong Implementability

  26. Conclusion NP-complete! • Strong Implementability in dominant strategiesÎNP • Characterizationresultgeneralizesto infinite type spaces • Open: Is theproblem in P? • Useful(?) results: • Augmented Revelation Principle • Selectiveeliminationprocedurewithpolynomiallymanysteps • Paymentsofpolynomialencodingsize Strong Implementability

  27. Thank you! Strong Implementability