Nash Equilibria on (Un)Stable Networks
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While individuals may selfishly choose their optimal behaviors (Nash, 1950), they commit to relationships that result from communication, coordination, and cooperation (Jackson and Wolinsky, 1996). In games of friendship links and behaviors, a Nash equilibrium in k-stable network (NEkSN) emerges when players internalize the consensual nature of human relationships. The joint choice of behaviors and relationships may result in a multitude of equilibria, ranked in probabilistic sense as these equilibria arise in a k-player consensual dynamic (kCD). Application of the proposed framework to adolescents' tobacco smoking and friendship decisions suggests that: (a.) the response of the friendship network to changes in tobacco price amplifies the intended effect on smoking, (b.) racially desegregating high-schools decreases the overall smoking prevalence, (c.) the response of the social network is quantitatively important in analyzing the aggregate spillovers, (d.) the estimation biases when the network externalities are mis-specified and when peer effects are omitted are of the same sign.
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