IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v25y2017i3d10.1007_s11750-017-0444-5.html
   My bibliography  Save this article

Equilibrium selection in multi-leader-follower games with vertical information

Author

Listed:
  • Maria Carmela Ceparano

    (University of Naples Federico II)

  • Jacqueline Morgan

    (University of Naples Federico II)

Abstract

We consider two-stage multi-leader-follower games, called multi-leader-follower games with vertical information, where leaders in the first stage and followers in the second stage choose simultaneously an action, but those chosen by any leader are observed by only one “exclusive” follower. This partial unobservability leads to extensive form games that have no proper subgames but may have an infinity of Nash equilibria. So it is not possible to refine using the concept of subgame perfect Nash equilibrium and, moreover, the concept of weak perfect Bayesian equilibrium could be not useful since it does not prescribe limitations on the beliefs out of the equilibrium path. This has motivated the introduction of a selection concept for Nash equilibria based on a specific class of beliefs, called passive beliefs, that each follower has about the actions chosen by the leaders rivals of his own leader. In this paper, we illustrate the effectiveness of this concept and we investigate the existence of such a selection for significant classes of problems satisfying generalized concavity properties and conditions of minimal character on possibly discontinuous data.

Suggested Citation

  • Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Equilibrium selection in multi-leader-follower games with vertical information," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 526-543, October.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:3:d:10.1007_s11750-017-0444-5
    DOI: 10.1007/s11750-017-0444-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-017-0444-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11750-017-0444-5?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. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. Heski Bar-Isaac & Guillermo Caruana & Vicente Cunat, 2012. "Search, Design, and Market Structure," American Economic Review, American Economic Association, vol. 102(2), pages 1140-1160, April.
    4. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    5. Eguia, Jon X. & Llorente-Saguer, Aniol & Morton, Rebecca & Nicolò, Antonio, 2018. "Equilibrium selection in sequential games with imperfect information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 465-483.
    6. Ceparano, Maria Carmela & Quartieri, Federico, 2017. "Nash equilibrium uniqueness in nice games with isotone best replies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 154-165.
    7. Alessandro Gavazza & Alessandro Lizzeri, 2009. "Transparency and Economic Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1023-1048.
    8. Oliver Hart & Jean Tirole, 1990. "Vertical Integration and Market Foreclosure," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 21(1990 Micr), pages 205-286.
    9. McAfee, R Preston & Schwartz, Marius, 1994. "Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity," American Economic Review, American Economic Association, vol. 84(1), pages 210-230, March.
    10. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    11. Jacques Cremer & Michael H. Riordan, 1987. "On Governing Multilateral Transactions with Bilateral Contracts," RAND Journal of Economics, The RAND Corporation, vol. 18(3), pages 436-451, Autumn.
    12. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
    13. Daniel P. O'Brien & Greg Shaffer, 1992. "Vertical Control with Bilateral Contracts," RAND Journal of Economics, The RAND Corporation, vol. 23(3), pages 299-308, Autumn.
    14. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    15. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    16. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    17. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
    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. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.

    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. Maria Carmela Ceparano & Jacqueline Morgan, 2015. "Equilibria Under Passive Beliefs for Multi-leader-follower Games with Vertical Information: Existence Results," CSEF Working Papers 417, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Jan 2017.
    2. Eguia, Jon X. & Llorente-Saguer, Aniol & Morton, Rebecca & Nicolò, Antonio, 2018. "Equilibrium selection in sequential games with imperfect information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 465-483.
    3. Bakaouka, Elpiniki & Milliou, Chrysovalantou, 2018. "Vertical licensing, input pricing, and entry," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 66-96.
    4. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    5. Chrysovalantou Milliou & Apostolis Pavlou, 2020. "Foreign direct investment in vertically related markets," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 284-320, February.
    6. Corts, Kenneth S. & Neher, Darwin V., 2003. "Credible delegation," European Economic Review, Elsevier, vol. 47(3), pages 395-407, June.
    7. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    8. Bjørn Olav Johansen & Tore Nilssen, 2016. "The Economics of Retailing Formats: Competition Versus Bargaining," Journal of Industrial Economics, Wiley Blackwell, vol. 64(1), pages 109-134, March.
    9. Pagnozzi, Marco & Piccolo, Salvatore & Reisinger, Markus, 2021. "Vertical contracting with endogenous market structure," Journal of Economic Theory, Elsevier, vol. 196(C).
    10. Michele Bisceglia & Jorge Padilla & Salvatore Piccolo, 2019. "When Prohibiting Platform Parity Agreements Harms Consumers," CSEF Working Papers 542, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    11. Doh‐Shin Jeon & Yassine Lefouili, 2018. "Cross‐licensing and competition," RAND Journal of Economics, RAND Corporation, vol. 49(3), pages 656-671, September.
    12. Hunold, Matthias & Schlütter, Frank, 2022. "Supply Contracts under Partial Forward Ownership," LIDAM Discussion Papers CORE 2022003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Simona Grassi & Ching-to Albert Ma, 2016. "Information acquisition, referral, and organization," RAND Journal of Economics, RAND Corporation, vol. 47(4), pages 935-960, November.
    14. Bisceglia, Michele & Padilla, Jorge & Piccolo, Salvatore, 2021. "When prohibiting wholesale price-parity agreements may harm consumers," International Journal of Industrial Organization, Elsevier, vol. 76(C).
    15. Janssen, Maarten C.W., 2020. "Vertical contracts in search markets," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    16. Claire Chambolle & Sofia Villas-Boas, 2007. "Buyer Power through Producer's Differentiation," Working Papers hal-00243058, HAL.
    17. Bisceglia, Michele & Padilla, Jorge & Piccolo, Salvatore & Shekhar, Shiva, 2022. "Vertical integration, innovation and foreclosure with competing ecosystems," Information Economics and Policy, Elsevier, vol. 60(C).
    18. Marx, Leslie M. & Shaffer, Greg, 2004. "Opportunism and menus of two-part tariffs," International Journal of Industrial Organization, Elsevier, vol. 22(10), pages 1399-1414, December.
    19. Maria Alipranti & Emmanuel Petrakis, 2022. "Upstream market structure and the timing of technology adoption," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(5), pages 1298-1310, July.
    20. Allain, Marie-Laure & Chambolle, Claire, 2011. "Anti-competitive effects of resale-below-cost laws," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 373-385, 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:topjnl:v:25:y:2017:i:3:d:10.1007_s11750-017-0444-5. 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.