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

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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.

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  • 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
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    1. 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.
    2. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    3. 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.
    4. 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.
    5. Marco Pagnozzi & Salvatore Piccolo, 2012. "Vertical Separation with Private Contracts," Economic Journal, Royal Economic Society, vol. 122(559), pages 173-207, March.
    6. 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.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    9. 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.
    10. 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.
    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.
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    Keywords

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