Endogenous Network Dynamics

46 Pages Posted: 18 Jul 2009

See all articles by Frank H. Page

Frank H. Page

Systemic Risk Centre, LSE; Indiana University, Bloomington - Department of Economics

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics

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Date Written: June 29, 2009

Abstract

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).

Keywords: Endogenous Network Dynamics, Dynamic Stochastic Games of Network Formation, Equilibrium Markov Process of Network Formation, Basins of Attraction, Harris Decomposition, Ergodic Probability Measures, Dynamic Path Dominance Core, Dynamic Pairwise Stability

JEL Classification: A14, C71, C72

Suggested Citation

Page, Frank H. and Wooders, Myrna H., Endogenous Network Dynamics (June 29, 2009). FEEM Working Paper No. 28.2009. Available at SSRN: https://ssrn.com/abstract=1427222 or http://dx.doi.org/10.2139/ssrn.1427222

Frank H. Page (Contact Author)

Systemic Risk Centre, LSE ( email )

Houghton St
London, WC2A 2AE
United Kingdom

HOME PAGE: http://www.systemicrisk.ac.uk/

Indiana University, Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

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