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Endogenous Network Dynamics

43 Pages Posted: 19 Feb 2009 Last revised: 16 Mar 2009

Frank H. Page Jr.

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

Myrna H. Wooders

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

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Date Written: February 9, 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 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).

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 (February 9, 2009). CAEPR Working Paper No. 002-2009. Available at SSRN: https://ssrn.com/abstract=1344439 or http://dx.doi.org/10.2139/ssrn.1344439

Frank H. Page Jr. (Contact Author)

Indiana University, Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Systemic Risk Centre, LSE ( email )

Houghton St
London, WC2A 2AE
United Kingdom

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

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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