Strategic complementarities, network games and endogenous network formation
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This paper investigates the role of strategic complementarities in the context of network games and network formation models. In the general model of static games on networks, we characterize conditions on the utility function that ensure the existence and uniqueness of a pure-strategy Nash equilibrium, regardless of the network structure. By applying the game to empirically-relevant networks that feature nestedness—Nested Split Graphs—we show that equilibrium strategies are non-decreasing in the degree. We extend the framework into a dynamic setting, comprising a game stage and a formation stage, and provide general conditions for the network process to converge to a Nested Split Graph with probability one, and for this class of networks to be an absorbing state. The general framework presented in the paper can be applied to models of games on networks, models of network formation, and combinations of the two.
KeywordsSocial networks Network formation Social interaction
We would like to thank Gabriel Carroll, Matthew O. Jackson, Michael D. König, Marco van der Leij, Ismael Y. Mourifié, Anna Larsson Seim, Yves Zenou and an anonymous referee for helpful comments and discussions as well as seminar participants at the MIT/Harvard Network Economics Workshop, the EEA meetings in 2010 and the SAET conference in 2012.
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