IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v206y2013i1p23-3710.1007-s10479-013-1334-3.html
   My bibliography  Save this article

Complexity of solution structures in nonlinear pricing

Author

Listed:
  • Kimmo Berg

Abstract

This paper characterizes and enumerates the possible solution structures in nonlinear pricing problem when the number of buyer types is given. It is shown that the single-crossing property, which is a standard assumption in the literature, reduces the complexity of solving the problem dramatically. The number of possible solution structures is important when the pricing problem is solved under limited information. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Kimmo Berg, 2013. "Complexity of solution structures in nonlinear pricing," Annals of Operations Research, Springer, vol. 206(1), pages 23-37, July.
    • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:23-37:10.1007/s10479-013-1334-3
    DOI: 10.1007/s10479-013-1334-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1334-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-013-1334-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andersson, Tommy, 2008. "Efficiency properties of non-linear pricing schedules without the single-crossing condition," Economics Letters, Elsevier, vol. 99(2), pages 364-366, May.
    2. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    3. Aaron S. Edlin & Chris Shannon, 1998. "Strict Single Crossing and the Strict Spence-Mirrlees Condition: A Comment on Monotone Comparative Statics," Econometrica, Econometric Society, vol. 66(6), pages 1417-1426, November.
    4. Ehtamo, Harri & Berg, Kimmo & Kitti, Mitri, 2010. "An adjustment scheme for nonlinear pricing problem with two buyers," European Journal of Operational Research, Elsevier, vol. 201(1), pages 259-266, February.
    5. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, November.
    6. Babu Nahata & Serguei Kokovin & Evgeny Zhelobodko, 2003. "Self-Selection Under Non-Ordered Valuations: Type-Splitting, Envy-Cycles, Rationing And Efficiency," General Economics and Teaching 0307001, University Library of Munich, Germany.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, November.
    9. A. Michael Spence, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 821-841.
    10. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    11. Andersson, Tommy, 2005. "Profit maximizing nonlinear pricing," Economics Letters, Elsevier, vol. 88(1), pages 135-139, July.
    12. Guesnerie, Roger & Seade, Jesus, 1982. "Nonlinear pricing in a finite economy," Journal of Public Economics, Elsevier, vol. 17(2), pages 157-179, March.
    13. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, November.
    14. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, November.
    15. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    16. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    17. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    18. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    19. Spence, Michael, 1977. "Nonlinear prices and welfare," Journal of Public Economics, Elsevier, vol. 8(1), pages 1-18, August.
    20. Kokovin, S. & Nahata, B. & Zhelobodko, E., 2011. "All Solution Graphs in Multidimensional Screening," Journal of the New Economic Association, New Economic Association, issue 11, pages 10-38.
    21. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, November.
    22. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, November.
    23. Kimmo Berg & Harri Ehtamo, 2012. "Continuous learning methods in two-buyer pricing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 287-304, June.
    24. Kimmo Berg & Harri Ehtamo, 2009. "Learning in nonlinear pricing with unknown utility functions," Annals of Operations Research, Springer, vol. 172(1), pages 375-392, November.
    25. Aloisio Pessoa_de_Araujo & Humberto L. Moreira, 2000. "Adverse Selection Problems without The Single Crossing Property," Econometric Society World Congress 2000 Contributed Papers 1874, Econometric Society.
    26. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics :theory and applications," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
    27. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    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. Arpita Roy & Shib Sankar Sana & Kripasindhu Chaudhuri, 2018. "Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model," Annals of Operations Research, Springer, vol. 260(1), pages 481-500, January.

    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. Kimmo Berg & Harri Ehtamo, 2012. "Continuous learning methods in two-buyer pricing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 287-304, June.
    2. Kelvin Shuangjian Zhang, 2019. "Existence in multidimensional screening with general nonlinear preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 463-485, March.
    3. Kelvin Shuangjian Zhang, 2017. "Existence in Multidimensional Screening with General Nonlinear Preferences," Papers 1710.08549, arXiv.org, revised Dec 2018.
    4. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    5. Prat, Andrea & Madarász, Kristóf, 2010. "Screening with an Approximate Type Space," CEPR Discussion Papers 7900, C.E.P.R. Discussion Papers.
    6. Dirk Bergemann & Ji Shen & Yun Xu & Edmund M. Yeh, 2012. "Multi-Dimensional Mechanism Design with Limited Information," Levine's Working Paper Archive 786969000000000559, David K. Levine.
    7. Pass, Brendan, 2012. "Convexity and multi-dimensional screening for spaces with different dimensions," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2399-2418.
    8. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    9. Barelli, Paulo & Basov, Suren & Bugarin, Mauricio & King, Ian King, 2010. "The Inclusiveness of Exclusion," Insper Working Papers wpe_211, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    10. Dirk Bergemann & Alessandro Pavan, 2015. "Introduction to JET Symposium Issue on "Dynamic Contracts and Mechanism Design"," Cowles Foundation Discussion Papers 2016, Cowles Foundation for Research in Economics, Yale University.
    11. Kristóf Madarász & Andrea Prat, 2017. "Sellers with Misspecified Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 790-815.
    12. Hoppe, Eva I. & Schmitz, Patrick W., 2015. "Do sellers offer menus of contracts to separate buyer types? An experimental test of adverse selection theory," Games and Economic Behavior, Elsevier, vol. 89(C), pages 17-33.
    13. Christian Moser & Pedro Olea de Souza e Silva, 2019. "Optimal Paternalistic Savings Policies," Opportunity and Inclusive Growth Institute Working Papers 17, Federal Reserve Bank of Minneapolis.
    14. Crawford, Gregory S & Shum, Matthew, 2007. "Monopoly Quality Degradation and Regulation in Cable Television," Journal of Law and Economics, University of Chicago Press, vol. 50(1), pages 181-219, February.
    15. Philipp Afèche & J. Michael Pavlin, 2016. "Optimal Price/Lead-Time Menus for Queues with Customer Choice: Segmentation, Pooling, and Strategic Delay," Management Science, INFORMS, vol. 62(8), pages 2412-2436, August.
    16. Paulo Barelli & Suren Basov & Mauricio Bugarin & Ian King, 2012. "The Robustness of Exclusion in Multi-dimensional Screening," RCER Working Papers 571, University of Rochester - Center for Economic Research (RCER).
    17. Harold Houba & Evgenia Motchenkova & Quan Wen, 2018. "Legal Principles in Antitrust Enforcement," Scandinavian Journal of Economics, Wiley Blackwell, vol. 120(3), pages 859-893, July.
    18. 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.
    19. Katsoulacos, Yannis & Motchenkova, Evgenia & Ulph, David, 2015. "Penalizing cartels: The case for basing penalties on price overcharge," International Journal of Industrial Organization, Elsevier, vol. 42(C), pages 70-80.
    20. Houba Harold & Motchenkova Evgenia & Wen Quan, 2015. "The Effects of Leniency on Cartel Pricing," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(2), pages 351-389, July.

    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:spr:annopr:v:206:y:2013:i:1:p:23-37:10.1007/s10479-013-1334-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.