(Translated by https://www.hiragana.jp/)
Participation constraints in discontinuous adverse selection models
IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-03758833.html
   My bibliography  Save this paper

Participation constraints in discontinuous adverse selection models

Author

Listed:
  • David Martimort

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Lars A. Stole

    (University of Chicago)

Abstract

We present a set of necessary and sufficient conditions for a class of optimal control problems with pure state constraints for which the objective function is linear in the state variable but the objective function is only required to be upper semicontinuous in the control variable. We apply those conditions to economic environments in contract theory where discontinuities in objectives prevail. Examples of applications include nonlinear pricing of digital goods and nonlinear pricing under competitive threat.

Suggested Citation

  • David Martimort & Lars A. Stole, 2022. "Participation constraints in discontinuous adverse selection models," Post-Print halshs-03758833, HAL.
    • Handle: RePEc:hal:journl:halshs-03758833
    DOI: 10.3982/TE3030
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Philippe Choné & Laurent Linnemer, 2015. "Nonlinear pricing and exclusion: I. buyer opportunism," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 217-240, June.
    2. Thomas, Lionel, 2001. "Cost functions in non-linear pricing," Economics Letters, Elsevier, vol. 72(1), pages 53-59, July.
    3. Lars A. Stole, 1995. "Nonlinear Pricing and Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(4), pages 529-562, December.
    4. Champsaur, Paul & Rochet, Jean-Charles, 1989. "Multiproduct Duopolists," Econometrica, Econometric Society, vol. 57(3), pages 533-557, May.
    5. Brainard, S. Lael & Martimort, David, 1997. "Strategic trade policy with incompletely informed policymakers," Journal of International Economics, Elsevier, vol. 42(1-2), pages 33-65, February.
    6. Martimort, David & Semenov, Aggey, 2008. "Ideological uncertainty and lobbying competition," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 456-481, April.
    7. Giacomo Calzolari & Vincenzo Denicol?, 2013. "Competition with Exclusive Contracts and Market-Share Discounts," American Economic Review, American Economic Association, vol. 103(6), pages 2384-2411, October.
    8. Cremer, Jacques & Khalil, Fahad & Rochet, Jean-Charles, 1998. "Contracts and Productive Information Gathering," Games and Economic Behavior, Elsevier, vol. 25(2), pages 174-193, November.
    9. Giacomo Calzolari & Vincenzo Denicolò, 2015. "Exclusive Contracts and Market Dominance," American Economic Review, American Economic Association, vol. 105(11), pages 3321-3351, November.
    10. Lewis Tracy R. & Sappington David E. M., 1993. "Ignorance in Agency Problems," Journal of Economic Theory, Elsevier, vol. 61(1), pages 169-183, October.
    11. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    12. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    13. repec:hal:pseose:hal-00813181 is not listed on IDEAS
    14. Biglaiser Gary & Mezzetti Claudio, 1993. "Principals Competing for an Agent in the Presence of Adverse Selection and Moral Hazard," Journal of Economic Theory, Elsevier, vol. 61(2), pages 302-330, December.
    15. Deb, Rahul & Said, Maher, 2015. "Dynamic screening with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 891-928.
    16. Carbajal, Juan Carlos & Ely, Jeffrey C., 2016. "A model of price discrimination under loss aversion and state-contingent reference points," Theoretical Economics, Econometric Society, vol. 11(2), May.
    17. Laffont, Jean-Jacques & Tirole, Jean, 1991. "Privatization and Incentives," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 7(0), pages 84-105, Special I.
    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. Caillaud, Bernard, 1990. "Regulation, competition, and asymmetric information," Journal of Economic Theory, Elsevier, vol. 52(1), pages 87-110, October.
    20. Ke-Wei Huang & Arun Sundararajan, 2011. "Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure," Information Systems Research, INFORMS, vol. 22(4), pages 721-738, December.
    21. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, vol. 76(2), pages 753-772.
    22. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    23. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    24. Nicolas Curien & Bruno Jullien & Patrick Rey, 1998. "Pricing Regulation Under Bypass Competition," RAND Journal of Economics, The RAND Corporation, vol. 29(2), pages 259-279, Summer.
    25. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    26. Claudio Mezzetti, 1997. "Common Agency with Horizontally Differentiated Principals," RAND Journal of Economics, The RAND Corporation, vol. 28(2), pages 323-345, Summer.
    27. David Martimort & Lars Stole, 2009. "Market participation in delegated and intrinsic common‐agency games," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 78-102, March.
    28. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    29. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    30. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    31. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    32. Aghion, Philippe & Bolton, Patrick, 1987. "Contracts as a Barrier to Entry," American Economic Review, American Economic Association, vol. 77(3), pages 388-401, June.
    33. Lewis, Tracy R. & Sappington, David E. M., 1989. "Countervailing incentives in agency problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 294-313, December.
    34. Ollier, Sandrine & Thomas, Lionel, 2013. "Ex post participation constraint in a principal–agent model with adverse selection and moral hazard," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2383-2403.
    35. Spulber, Daniel F, 1993. "Monopoly Pricing of Capacity Usage under Asymmetric Information," Journal of Industrial Economics, Wiley Blackwell, vol. 41(3), pages 241-257, September.
    36. Maggi G. & Rodriguez-Clare A., 1995. "On Countervailing Incentives," Journal of Economic Theory, Elsevier, vol. 66(1), pages 238-263, June.
    37. Laffont, Jean-Jacques & Tirole, Jean, 1990. "Optimal Bypass and Cream Skimming," American Economic Review, American Economic Association, vol. 80(5), pages 1042-1061, December.
    38. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Julian Teichgräber & Simon Žužek & Jannik Hensel, 2022. "Optimal short-time work: screening for jobs at risk," ECON - Working Papers 402, Department of Economics - University of Zurich.

    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. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
    2. Martimort, David & Stole, Lars, 2011. "Public Contracting in Delegated Agency Games," MPRA Paper 32874, University Library of Munich, Germany.
    3. Armstrong, Mark & Sappington, David E.M., 2007. "Recent Developments in the Theory of Regulation," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 27, pages 1557-1700, Elsevier.
    4. Marinovic, Iván & Povel, Paul, 2017. "Competition for talent under performance manipulation," Journal of Accounting and Economics, Elsevier, vol. 64(1), pages 1-14.
    5. Martimort, David & Semenov, Aggey & Stole, Lars A., 2018. "A complete characterization of equilibria in an intrinsic common agency screening game," Theoretical Economics, Econometric Society, vol. 13(3), September.
    6. Bannier, Christina E. & Feess, Eberhard & Packham, Natalie, 2014. "Incentive schemes, private information and the double-edged role of competition for agents," CFS Working Paper Series 475, Center for Financial Studies (CFS).
    7. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    8. Olsen, Trond E. & Osmundsen, Petter, 2011. "Multinationals, tax competition and outside options," Journal of Public Economics, Elsevier, vol. 95(11), pages 1579-1588.
    9. Hector Chade & Jeroen Swinkels, 2021. "Screening in Vertical Oligopolies," Econometrica, Econometric Society, vol. 89(3), pages 1265-1311, May.
    10. David Martimort & Aggey Semenov & Lars Stole, 2016. "A Complete Characterization of Equilibria in Common Agency Screening Games," Working Papers 1618E, University of Ottawa, Department of Economics.
    11. Jensen, S., 2000. "Price Discrimination and Three Part Tariffs in a Duopoly," Papers 3/2000, Norwegian School of Economics and Business Administration-.
    12. Hernández-Murillo, Rubén, 2019. "Interjurisdictional competition with adverse selection," Journal of Public Economics, Elsevier, vol. 173(C), pages 85-95.
    13. Inderst, Roman, 2004. "Contractual distortions in a market with frictions," Journal of Economic Theory, Elsevier, vol. 116(1), pages 155-176, May.
    14. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    15. Noldeke,G. & Samuelson,L., 2004. "Decomposable principal-agent problems," Working papers 14, Wisconsin Madison - Social Systems.
    16. Alasseur, Clémence & Chaton, Corinne & Hubert, Emma, 2022. "Optimal contracts under adverse selection for staple goods such as energy: Effectiveness of in-kind insurance," Energy Economics, Elsevier, vol. 106(C).
    17. Christina E. Bannier & Eberhard Feess & Natalie Packham & Markus Walzl, 2021. "Differentiation and Risk Aversion in Imperfectly Competitive Labor Markets," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 177(1), pages 1-27.
    18. Ruiz del Portal, X., 2009. "A general principal-agent setting with non-differentiable mechanisms: Some examples," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 262-278, March.
    19. Martimort, David & Stole, Lars, 2015. "Menu Auctions and Influence Games with Private Information," MPRA Paper 62388, University Library of Munich, Germany.
    20. Burani, Nadia & Mantovani, Andrea, 2020. "Non-linear pricing and conscious consumption," International Journal of Industrial Organization, Elsevier, vol. 68(C).

    More about this item

    Keywords

    Optimal control; Nonsmooth optimization; Convex analysis; Type-dependent participation constraints; Principal-agent models;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

    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:hal:journl:halshs-03758833. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.