Nash Equilibria on k-stable Networks

Anton Badev

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"[the distinction between cooperative and non-cooperative games] depends on the possibility or impossibility of coalitions, communications, and side-payments." (Nash, 1950)


While individuals may choose their optimal behaviors selfishly only considering their own incentives (Nash, 1950), they commit to relationships that result from communication, coordination, and collaboration (Jackson and Wolinsky, 1996).

I consider a discrete game on endogenous network where players jointly choose behaviors and friendship links. A Nash equilibrium in a k-stable (NEkS) network emerges when players internalize the need for consensus in forming friendships. A primitive of these games is payoff externalities and the possibility for multiple NEkS networks. NEkS networks are ranked in probabilistic sense as they arise in a k-player consensual dynamic (kCD). Properties of kCD fascilitate simulation from and estimation of these games.

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 analysis of peer effects and aggregate spillovers is impacted by either the response of the friendship network or lack of social network data in important ways.

Preferences over tobacco smoking and frienships


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