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Endogenous Network Dynamics

  • Frank H. Page, Jr.

    ()

    (Indiana University)

  • Myrna H. Wooders

    ()

    (Vanderbilt University)

In all social and economic interactions, individuals or coalitions choose not only with whom to interact but how to interact, and over time both the structure (the “with whom”) and the strategy (“the how”) of interactions change. Our objectives here are to model the structure and strategy of interactions prevailing at any point in time as a directed network and to address the following open question in the theory of social and economic network formation: given the rules of network and coalition formation, the preferences of individuals over networks, the strategic behavior of coalitions in forming networks, and the trembles of nature, what network and coalitional dynamics are likely to emergence and persist. Our main contributions are (i) to formulate the problem of network and coalition formation as a dynamic, stochastic game, (ii) to show that this game possesses a stationary correlated equilibrium (in network and coalition formation strategies), (iii) to show that, together with the trembles of nature, this stationary correlated equilibrium determines an equilibrium Markov process of network and coalition formation which respects the rules of network and coalition formation and the preferences of individuals, and (iv) to show that, although uncountably many networks may form, this endogenous process of network and coalition formation possesses a nonempty finite set of ergodic measures and generates a finite, disjoint collection of nonempty subsets of networks and coalitions, each constituting a basin of attraction. Moreover, we extend to the setting of endogenous Markov dynamics the notions of pairwise stability (Jackson-Wolinsky, 1996), strong stability (Jackson-van den Nouweland, 2005), and Nash stability (Bala-Goyal, 2000), and we show that in order for any network-coalition pair to be stable (pairwise, strong, or Nash) it is necessary and sufficient that the pair reside in one of finitely many basins of attraction - and hence reside in the support of an ergodic measure. The results we obtain here for endogenous network dynamics and stochastic basins of attraction are the dynamic analogs of our earlier results on endogenous network formation and strategic basins of attraction in static, abstract games of network formation (Page and Wooders, 2008), and build on the seminal contributions of Jackson and Watts (2002), Konishi and Ray (2003), and Dutta, Ghosal, and Ray (2005).

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File URL: http://www.iub.edu/~caepr/RePEc/PDF/2009/CAEPR2009-002.pdf
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Paper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2009-002.

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Length: 45 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:inu:caeprp:2009-002
Contact details of provider: Postal: 812-855-1021
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Web page: http://www.iub.edu/~caepr
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  1. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Matthew O. Jackson & Anne van den Nouweland, 2002. "Strongly Stable Networks," Microeconomics 0211006, EconWPA.
  3. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  4. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
  5. Page Jr, Frank H & Wooders, Myrna H, 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," The Warwick Economics Research Paper Series (TWERPS) 724, University of Warwick, Department of Economics.
  6. Mertens, J.-F. & Neyman, A., . "Stochastic games," CORE Discussion Papers RP -454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  8. Page Jr, Frank H & Wooders, Myrna H. & Kamat, Samir, 2002. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 660, University of Warwick, Department of Economics.
  9. AMIR, Rabah & LAMBSON, Val E., . "Entry, exit, and imperfect competition in the long run," CORE Discussion Papers RP -1651, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  11. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  12. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  13. Frank H. Page, Jr. & Myrna H. Wooders, 2006. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Vanderbilt University Department of Economics Working Papers 0614, Vanderbilt University Department of Economics.
  14. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
  15. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer, vol. 66(3), pages 513-530, December.
  16. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
  17. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
    • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  19. Costa, O.L.V. & Dufour, F., 2005. "On the ergodic decomposition for a class of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 401-415, March.
  20. 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.
  21. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
  22. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," CORE Discussion Papers 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. 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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