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Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities

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  • Artem Sedakov

    (Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University,7/9 Universitetskaya nab., Saint Petersburg 199034, Russia
    School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    Institute of Applied Mathematics of Shandong, Qingdao 266071, China)

Abstract

Time consistency is a property of the solution to a cooperative dynamic game which guarantees that this solution remains stable with respect to its revision by players over time. The fulfillment of this property is directly related to the characteristic function and its behavior with the course of the game as any solution is based on this function. In this paper, we will examine the characteristic functions for two economic models with network externalities represented by a two-stage network game using the theory developed for this class of games. For a network game with positive externalities represented by a public goods provision model, we demonstrate a sufficient condition for time consistency. For a network game with negative externalities represented by a market competition model, we show that the cooperative solution is always time consistent.

Suggested Citation

  • Artem Sedakov, 2020. "Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:38-:d:304033
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    References listed on IDEAS

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    1. Pascal Billand & Christophe Bravard & Jacques Durieu & Sudipta Sarangi, 2019. "Firm Heterogeneity And The Pattern Of R&D Collaborations," Economic Inquiry, Western Economic Association International, vol. 57(4), pages 1896-1914, October.
    2. Driessen, Theo S.H. & Meinhardt, Holger I., 2005. "Convexity of oligopoly games without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 102-126, July.
    3. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    4. Zhao, Jingang, 1999. "A necessary and sufficient condition for the convexity in oligopoly games," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 189-204, March.
    5. Andrea Galeotti & Sanjeev Goyal, 2010. "The Law of the Few," American Economic Review, American Economic Association, vol. 100(4), pages 1468-1492, September.
    6. Nizar Allouch & Maia King, 2019. "Constrained public goods in networks," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(5), pages 895-902, October.
    7. Pandit, Parthe & Kulkarni, Ankur A., 2018. "Refinement of the equilibrium of public goods games over networks: Efficiency and effort of specialized equilibria," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 125-139.
    8. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
    9. Rajan, Roby, 1989. "Endogenous Coalition Formation in Cooperative Oligopolies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 863-876, November.
    10. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
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    Cited by:

    1. Artem Sedakov & Hao Sun, 2020. "The Relationship between the Core and the Modified Cores of a Dynamic Game," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    2. Daniel Gómez & Javier Castro & Inmaculada Gutiérrez & Rosa Espínola, 2021. "A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection," Mathematics, MDPI, vol. 9(21), pages 1-29, October.

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