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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
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  1. MERTENS, Jean-François & PARTHASARATHY, T., . "Equilibria for discounted stochastic games," CORE Discussion Papers RP -1666, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  3. 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.
  4. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
  5. 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.
  6. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
  7. Amir, Rabah & Lambson, Val E., 2003. "Entry, exit, and imperfect competition in the long run," Journal of Economic Theory, Elsevier, vol. 110(1), pages 191-203, May.
  8. Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. 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.
  10. 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.
  11. Matthew O. Jackson & Anne van den Nouweland, 2002. "Strongly Stable Networks," Microeconomics 0211006, EconWPA.
  12. Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
  13. Bhaskar Dutta & Sayantan Ghosal & Debraj Ray, 2004. "Farsighted Network Formation," Working papers 122, Centre for Development Economics, Delhi School of Economics.
  14. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
  15. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  16. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP -1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Frank H. Page, Jr. & Myrna H. Wooders, 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," Working Papers 2005.36, Fondazione Eni Enrico Mattei.
  18. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  19. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  20. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer, vol. 66(3), pages 513-530, December.
  21. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
  22. 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).
  23. 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, .
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