IDEAS home Printed from https://ideas.repec.org/p/sef/csefwp/417.html
   My bibliography  Save this paper

Equilibria Under Passive Beliefs for Multi-leader-follower Games with Vertical Information: Existence Results

Author

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, 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.
    • Handle: RePEc:sef:csefwp:417
    as

    Download full text from publisher

    File URL: http://www.csef.it/WP/wp417.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    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. 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.
    4. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    5. 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.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    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. 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.
    9. 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.
    10. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    11. 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.
    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. 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.
    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. Jeanine Miklós-Thal & Greg Shaffer, 2016. "Naked Exclusion with Private Offers," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 174-194, November.
    5. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    6. 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.
    7. Corts, Kenneth S. & Neher, Darwin V., 2003. "Credible delegation," European Economic Review, Elsevier, vol. 47(3), pages 395-407, June.
    8. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    9. Emanuele Bacchiega & Olivier Bonroy, 2021. "Secret contracting and Nash-in-Nash bargaining," SN Business & Economics, Springer, vol. 1(11), pages 1-7, November.
    10. Milliou, Chrysovalantou & Petrakis, Emmanuel, 2007. "Upstream horizontal mergers, vertical contracts, and bargaining," International Journal of Industrial Organization, Elsevier, vol. 25(5), pages 963-987, October.
    11. 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.
    12. Moellers, Claudia & Normann, Hans-Theo & Snyder, Christopher M., 2017. "Communication in vertical markets: Experimental evidence," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 214-258.
    13. Pagnozzi, Marco & Piccolo, Salvatore & Reisinger, Markus, 2021. "Vertical contracting with endogenous market structure," Journal of Economic Theory, Elsevier, vol. 196(C).
    14. Alipranti, Maria & Milliou, Chrysovalantou & Petrakis, Emmanuel, 2014. "Price vs. quantity competition in a vertically related market," Economics Letters, Elsevier, vol. 124(1), pages 122-126.
    15. Michael Polemis & Konstantinos Eleftheriou, 2018. "To Regulate Or To Deregulate? The Role Of Downstream Competition In Upstream Monopoly Vertically Linked Markets," Bulletin of Economic Research, Wiley Blackwell, vol. 70(1), pages 51-63, January.
    16. Vanessa von Schlippenbach & Isabel Teichmann, 2012. "The Strategic Use of Private Quality Standards in Food Supply Chains," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(5), pages 1189-1201.
    17. 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.
    18. Tommy Staahl Gabrielsen & Bjørn Olav Johansen, 2017. "Resale Price Maintenance with Secret Contracts and Retail Service Externalities," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 63-87, February.
    19. Doh‐Shin Jeon & Yassine Lefouili, 2018. "Cross‐licensing and competition," RAND Journal of Economics, RAND Corporation, vol. 49(3), pages 656-671, September.
    20. 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).

    More about this item

    Keywords

    multi-leader-follower game; selection of equilibria; passive belief; discontinuous function; fixed point; generalized concavity;
    All these keywords.

    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:sef:csefwp:417. 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: Dr. Maria Carannante (email available below). General contact details of provider: https://edirc.repec.org/data/cssalit.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.