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Endogenous Network Dynamics

  • Frank H. Page

    (Indiana University)

  • Myrna H. Wooders

    (University of Warwick)

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 emerge 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, and (iv) to show that this endogenous process possesses a finite, nonempty set of ergodic measures, and generates a finite, disjoint collection of nonempty subsets of networks and coalitions, each constituting a basin of attraction. We also extend to the setting of endogenous Markov dynamics the notions of pairwise stability (Jackson-Wolinsky, 1996), strong stability (Jacksonvan den Nouweland, 2005), and Nash stability (Bala-Goyal, 2000), and we show that in order for any network-coalition pair to persist and be stable (pairwise, strong, or Nash) it is necessary and sufficient that the pair reside in one of finitely many basins of attraction. 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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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2009.28.

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Date of creation: May 2009
Date of revision:
Handle: RePEc:fem:femwpa:2009.28
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  1. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP 1587, 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. Bhaskar Dutta & Sayantan Ghosal & Debraj Ray, 2004. "Farsighted Network Formation," Working papers 122, Centre for Development Economics, Delhi School of Economics.
  4. 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.
  5. 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).
  6. Page Jr. Frank H & Wooders, Myrna & Kamat, Samir, 2003. "Networks and Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 689, University of Warwick, Department of Economics.
  7. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
  8. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  9. AMIRÂ , Rabah, 1995. "Continuous Stochastic Games of Capital Accumulation with Convex Transition," CORE Discussion Papers 1995009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
  11. Jackson, Matthew O. & van den Nouweland, Anne, 2002. "Strongly Stable Networks," Working Papers 1147, California Institute of Technology, Division of the Humanities and Social Sciences.
  12. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
  13. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  14. 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.
  15. 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.
  16. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer, vol. 66(3), pages 513-530, December.
  17. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
  19. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  20. AMIR, Rabah & LAMBSON, Val, 2003. "Entry, exit, and imperfect competition in the long run," CORE Discussion Papers 2003066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  22. 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.
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