IDEAS home Printed from https://ideas.repec.org/p/bsl/wpaper/2015-01.html
   My bibliography  Save this paper

The Implementation Duality

Author

Listed:
  • Nöldeke, Georg

    (University of Basel)

  • Samuelson, Larry

Abstract

We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear utility. We formulate and characterize a basic underlying implementation duality. We show how this duality can be used to obtain a sharpening of the taxation principle, to obtain a general existence result for solutions to the principal-agent problem, to show that (just as in the quasilinear case) all increasing decision functions are implementable under a single crossing condition, and to obtain an existence result for stable outcomes featuring positive assortative matching in a matching model.

Suggested Citation

  • Nöldeke, Georg & Samuelson, Larry, 2015. "The Implementation Duality," Working papers 2015/01, Faculty of Business and Economics - University of Basel.
    • Handle: RePEc:bsl:wpaper:2015/01
    as

    Download full text from publisher

    File URL: https://edoc.unibas.ch/61331/1/20180306103005_5a9e5f9d53663.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Strausz, Roland, 2006. "Deterministic versus stochastic mechanisms in principal-agent models," Journal of Economic Theory, Elsevier, vol. 128(1), pages 306-314, May.
    2. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    3. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    4. Kahn Charles M., 1993. "Existence and Characterization of Optimal Employment Contracts on a Continuous State Space," Journal of Economic Theory, Elsevier, vol. 59(1), pages 122-144, February.
    5. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    7. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    8. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    9. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    10. B. Monjardet, 1978. "An Axiomatic Theory of Tournament Aggregation," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 334-351, November.
    11. J. T. Chang & D. Pollard, 1997. "Conditioning as disintegration," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 287-317, November.
    12. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461, September.
    13. Balder, Erik J., 1996. "On the Existence of Optimal Contract Mechanisms for Incomplete Information Principal-Agent Models," Journal of Economic Theory, Elsevier, vol. 68(1), pages 133-148, January.
    14. Hector Chade & Jan Eeckhout & Lones Smith, 2017. "Sorting through Search and Matching Models in Economics," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 493-544, June.
    15. Hellwig, Martin, 1992. "Fully revealing outcomes in signalling models: An example of nonexistence when the type space is unbounded," Journal of Economic Theory, Elsevier, vol. 58(1), pages 93-104, October.
    16. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368, September.
    17. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    18. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    19. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    20. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    21. Peter Bardsley, 2012. "Duality in Contracting," Department of Economics - Working Papers Series 1141, The University of Melbourne.
    22. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    23. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    24. Carlier, Guillaume, 2001. "A general existence result for the principal-agent problem with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 129-150, February.
    25. Glosten, Lawrence R, 1989. "Insider Trading, Liquidity, and the Role of the Monopolist Specialist," The Journal of Business, University of Chicago Press, vol. 62(2), pages 211-235, April.
    26. Dworczak, Piotr & Zhang, Anthony Lee, 2017. "Implementability, Walrasian equilibria, and efficient matchings," Economics Letters, Elsevier, vol. 153(C), pages 57-60.
    27. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    28. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    29. Ivar Ekeland, 2010. "Notes on optimal transportation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 437-459, February.
    30. Jacob K. Goeree & Alexey Kushnir, 2011. "A geometric approach to mechanism design," ECON - Working Papers 056, Department of Economics - University of Zurich, revised Jun 2013.
    31. Weibull, Jorgen W., 1989. "A note on the continuity of incentive schedules," Journal of Public Economics, Elsevier, vol. 39(2), pages 239-243, July.
    32. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    33. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    2. Martimort, David & Stole, Lars A., 2022. "Participation constraints in discontinuous adverse selection models," Theoretical Economics, Econometric Society, vol. 17(3), July.
    3. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    4. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    5. , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    6. Andrea Attar & Thomas Mariotti & François Salanié, 2021. "Entry-Proofness and Discriminatory Pricing under Adverse Selection," American Economic Review, American Economic Association, vol. 111(8), pages 2623-2659, August.
    7. Andrea Attar & Thomas Mariotti & François Salanié, 2017. "Private Information and Insurance Rejections: A Comment," CEIS Research Paper 403, Tor Vergata University, CEIS, revised 03 May 2017.
    8. Mailath, George J. & Nöldeke, Georg, 2006. "Extreme Adverse Selection, Competitive Pricing, and Market Breakdown," Working papers 2006/09, Faculty of Business and Economics - University of Basel.
    9. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    10. Mailath, George J. & Nöldeke, Georg, 2008. "Does competitive pricing cause market breakdown under extreme adverse selection?," Journal of Economic Theory, Elsevier, vol. 140(1), pages 97-125, May.
    11. Jacob K. Goeree & Alexey Kushnir, 2011. "On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems," ECON - Working Papers 021, Department of Economics - University of Zurich.
    12. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.
    13. Suren Basov, 2002. "A Partial Characterization of the Solution of the Multidimensional Screening Problem with Nonlinear Preferences," Department of Economics - Working Papers Series 860, The University of Melbourne.
    14. Araujo, A. & Moreira, H. & Vieira, S., 2015. "The marginal tariff approach without single-crossing," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 166-184.
    15. Levent Ülkü, 2014. "Mechanism design without monotone differences: an example featuring buyer habits," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 183-195, October.
    16. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.
    17. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2019. "On competitive nonlinear pricing," Theoretical Economics, Econometric Society, vol. 14(1), January.
    18. André Berger & Rudolf Müller & Seyed Hossein Naeemi, 2017. "Characterizing implementable allocation rules in multi-dimensional environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 367-383, February.
    19. Garrett, Daniel F., 2020. "Payoff Implications of Incentive Contracting," TSE Working Papers 20-1140, Toulouse School of Economics (TSE).
    20. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.

    More about this item

    Keywords

    Implementation; Duality; Galois Connection; Imperfectly Transferable Utility; Principal-Agent Model; Two-Sided Matching;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bsl:wpaper:2015/01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: WWZ (email available below). General contact details of provider: https://edirc.repec.org/data/wwzbsch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.