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Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions

Author

Listed:
  • Jing Fu

    (Fukuoka Institute of Technology
    London School of Economics and Political Science)

  • Frank Page

    (London School of Economics and Political Science
    Indiana University)

  • Jean-Pierre Zigrand

    (London School of Economics and Political Science
    London School of Economics and Political Science)

Abstract

An important aspect of network dynamics that has been missing from our understanding of network dynamics in various applied settings is the influence of strategic behavior in determining equilibrium network dynamics. Our main objective hears to say what we can regarding the emergence of stable club networks—and therefore, stable coalition structures—based on the stability properties of strategically determined equilibrium network formation dynamics. Because club networks are layered networks, our work here can be thought of as a first work on the strategic dynamics of layered networks. In addition to constructing a discounted stochastic game model (i.e., a DSG model) of club network formation, (1) we show that our DSG of network formation possesses a stationary Markov perfect equilibrium in players’ membership-action strategies; (2) we identify the assumptions on primitives which ensure that the induced equilibrium Markov process of layered club network formation satisfies the Tweedie Stability Conditions (Tweedie in Stoch Processes Their Appl 92:345–354) and (3) we show that, as a consequence, the equilibrium Markov network formation process generates a unique decomposition of the set of state-network pairs into a transient set together with finitely many basins of attraction. Moreover, we show that if there is a basin containing a vio set (a visited infinitely often set) of club networks sufficiently close together, then the coalition structures across club networks in the vio set will be the same (i.e., closeness across networks in a vio set leads to invariance in coalition structure across networks in a vio set).

Suggested Citation

  • Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 669-704, June.
  • Handle: RePEc:spr:dyngam:v:13:y:2023:i:2:d:10.1007_s13235-022-00483-7
    DOI: 10.1007/s13235-022-00483-7
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    References listed on IDEAS

    as
    1. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
    2. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
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    4. He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    5. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
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    8. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 265-281, April.
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    11. Tweedie, R. L., 2001. "Drift conditions and invariant measures for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 345-354, April.
    12. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
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    14. Wei He & Yeneng Sun, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," Papers 1311.1562, arXiv.org, revised Jan 2017.
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    More about this item

    Keywords

    Club networks; Stable coalition structures; Harris recurrent sets; Topological Harris recurrent sets; Basins of attraction; Discounted stochastic games; Stationary Markov perfect equilibria;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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