Endogenous Correlated Network Dynamics

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Working paper
Frank Page, Rui Gong and Myrna Wooders
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Vanderbilt University Department of Economics Working Papers
Vanderbilt University
We model the structure and strategy of social interactions prevailing at any point in time as a directed network and address the following question: given the rules of network and coalition formation, preferences of individuals over networks, strategic behavior of coalitions in forming networks, and the trembles of nature, what network and coalitional dynamics are likely to emergence and persist. We formulate the problemas a dynamic, stochastic game and v equilibrium (in network and coalition formation strategies), (ii) together with the trembles of nature, this correlated stationary equilibrium determines an equilibrium Markov process of network and coalition formation, and (iii) this endogenous Markov process possesses a 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) and the path dominance core (Page Wooders, 2009a). We show that in order for any network-coalition pair to emerge and persist, it is necessary that the pair reside in one of finitely many basins of attraction. The results we obtain here build on Page and Wooders (2009a)and the seminal contributions of Jackson and Watts (2002), Konishi and Ray (2003), and Dutta, Ghosal, and Ray (2005).
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