IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v231y2026ics0022053125001735.html

Intertemporal bundling

Author

Listed:
  • Lu, Jingfeng
  • Zhao, Wenbo

Abstract

This paper studies when and how intertemporal bundling arises in optimal dynamic selling mechanisms in a two-period setting, where two objects (A and B) are sequentially available for sale. When the buyer’s values of the two objects (vA and vB respectively) are independent, in contrast to conventional insight from simultaneous sales, we find in our setting that there is no loss in relying on separate sales for optimal design. This result extends under widely adopted regularity conditions when the values are positively correlated in the sense that vB is stochastically increasing in vA. However, if vB is stochastically decreasing in vA, separate sales are no longer optimal, and the optimal integrated design features intertemporal bundling. When it is always efficient to provide each good, the optimal selling mechanism is implemented by offering a menu of intertemporal bundles with different prices, where each bundle consists of the second object together with a probabilistic proportion of the first object. In particular, if the buyer’s virtual value of the first good is always non-negative, pure bundling becomes optimal.

Suggested Citation

  • Lu, Jingfeng & Zhao, Wenbo, 2026. "Intertemporal bundling," Journal of Economic Theory, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:jetheo:v:231:y:2026:i:c:s0022053125001735
    DOI: 10.1016/j.jet.2025.106127
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053125001735
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2025.106127?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Baron, David P. & Besanko, David, 1984. "Regulation and information in a continuing relationship," Information Economics and Policy, Elsevier, vol. 1(3), pages 267-302.
    3. Indranil Chakraborty, 1999. "Bundling decisions for selling multiple objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 723-733.
    4. Zhou, Jidong, 2021. "Mixed bundling in oligopoly markets," Journal of Economic Theory, Elsevier, vol. 194(C).
    5. Krähmer, Daniel & Strausz, Roland, 2017. "Sequential versus static screening: An equivalence result," Games and Economic Behavior, Elsevier, vol. 106(C), pages 317-328.
    6. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel Y., 2020. "The scope of sequential screening with ex post participation constraints," Journal of Economic Theory, Elsevier, vol. 188(C).
    7. Daniel Krähmer & Roland Strausz, 2015. "Optimal Sales Contracts with Withdrawal Rights," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(2), pages 762-790.
    8. 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.
    9. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
    10. Mark Armstrong, 2000. "Optimal Multi-Object Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 455-481.
    11. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 371-383.
    12. Battaglini, Marco & Lamba, Rohit, 2019. "Optimal dynamic contracting: the first-order approach and beyond," Theoretical Economics, Econometric Society, vol. 14(4), November.
    13. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    14. Daniel Krähmer & Roland Strausz, 2011. "Optimal Procurement Contracts with Pre-Project Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(3), pages 1015-1041.
    15. Pavlov Gregory, 2011. "Optimal Mechanism for Selling Two Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-35, February.
    16. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    17. Meng, Dawen & Sun, Lei & Tian, Guoqiang, 2022. "Dynamic mechanism design on social networks," Games and Economic Behavior, Elsevier, vol. 131(C), pages 84-120.
    18. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
    19. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    20. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    21. Alessandro Pavan & Ilya Segal & Juuso Toikka, 2014. "Dynamic Mechanism Design: A Myersonian Approach," Econometrica, Econometric Society, vol. 82(2), pages 601-653, March.
    22. William James Adams & Janet L. Yellen, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(3), pages 475-498.
    23. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    24. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    25. Riordan, Michael H & Sappington, David E M, 1987. "Awarding Monopoly Franchises," American Economic Review, American Economic Association, vol. 77(3), pages 375-387, June.
    26. Stigler, George J., 1983. "The Organization of Industry," University of Chicago Press Economics Books, University of Chicago Press, number 9780226774329, August.
    27. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    28. Liu, Bin & Liu, Dongri & Lu, Jingfeng, 2020. "Shifting supports in Esö and Szentes (2007)," Economics Letters, Elsevier, vol. 193(C).
    29. Pascal Courty & Li Hao, 2000. "Sequential Screening," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(4), pages 697-717.
    30. Jidong Zhou, 2017. "Competitive Bundling," Econometrica, Econometric Society, vol. 85, pages 145-172, January.
    31. Raphael Boleslavsky & Maher Said, 2013. "Progressive Screening: Long-Term Contracting with a Privately Known Stochastic Process," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 1-34.
    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. Meng, Dawen & Sun, Lei & Tian, Guoqiang, 2022. "Dynamic mechanism design on social networks," Games and Economic Behavior, Elsevier, vol. 131(C), pages 84-120.
    2. Rochet, Jean-Charles, 2024. "Multidimensional screening after 37 years," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    3. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    4. Huiyi Guo & Wei He & Bin Liu, 2022. "Learning by Consuming: Optimal Pricing with Endogenous Information Provision," Papers 2209.01453, arXiv.org.
    5. Chifeng Dai, 2021. "Optimal sequential contract with a risk‐averse supplier," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 92-125, February.
    6. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    7. Liu, Bin & Liu, Dongri & Lu, Jingfeng, 2020. "Shifting supports in Esö and Szentes (2007)," Economics Letters, Elsevier, vol. 193(C).
    8. Krähmer, Daniel & Strausz, Roland, 2017. "Sequential versus static screening: An equivalence result," Games and Economic Behavior, Elsevier, vol. 106(C), pages 317-328.
    9. Liu, Dongri & Lu, Jingfeng, 2025. "An implementation of the general optimal mechanism in Esö and Szentes (2007)," Games and Economic Behavior, Elsevier, vol. 151(C), pages 82-94.
    10. Boaz Zik, 2023. "Efficient sequential screening with informational externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 567-590, February.
    11. Arve, Malin & Martimort, David, 2023. "Auctioning Long-Term Projects under Financial Constraints," TSE Working Papers 23-1469, Toulouse School of Economics (TSE), revised May 2024.
    12. Terstiege, Stefan, 2016. "Gathering imperfect information before signing a contract," Games and Economic Behavior, Elsevier, vol. 97(C), pages 70-87.
    13. Daniel Danau & Annalisa Vinella, 2016. "Sequential screening and the relationship between principal's preferences and agent's incentives," SERIES 01-2016, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Mar 2016.
    14. Chen, Bo & Ni, Debing, 2017. "Optimal bundle pricing under correlated valuations," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 248-281.
    15. Szalay, Dezső & Ketelaar, Felix, 2014. "Pricing a Package of Services," CEPR Discussion Papers 10313, Centre for Economic Policy Research.
    16. Di Corato, Luca & Moretto, Michele, 2026. "Dynamic Adverse Selection with Flow Limited Liability: A Closed-Form Approach to Price Regulation," FEEM Working Papers 396239, Fondazione Eni Enrico Mattei (FEEM).
    17. Zhenyu Hu & Yangge Xiao, 2025. "Optimal Dynamic Mechanism Under Customer Search," Operations Research, INFORMS, vol. 73(4), pages 2045-2060, July.
    18. Ketelaar, Felix & Szalay, Dezsö, 2014. "Pricing a Package of Services - When (not) to bundle," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 487, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    19. Jean‐Charles Rochet & John Thanassoulis, 2019. "Intertemporal price discrimination with two products," RAND Journal of Economics, RAND Corporation, vol. 50(4), pages 951-973, December.
    20. Chang, Dongkyu, 2021. "Optimal sales mechanism with outside options," Journal of Economic Theory, Elsevier, vol. 195(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • 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:eee:jetheo:v:231:y:2026:i:c:s0022053125001735. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.