Nash Equilibria on k-stable Networks

Anton Badev

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In response to a change, individuals may choose to follow the responses of their friends or, alternatively, to change their friends. To model these decisions, consider a game where players jointly choose their behaviors and friendships. While players choose their behaviors selfishly only considering their own incentives (Nash, 1950), their choice of friendships presumes consent (Jackson and Wolinsky, 1996).

A Nash equilibrium in a k-stable (NEkS) network emerges when players internalize the need for consensus in forming friendships. In these equilibria, players choose their optimal strategies on subsets of k players - a form of bounded rationality. The k-player consensual dynamic delivers a probabilistic ranking of a game's equilibria, and, via a varying k, facilitates estimation of such games.

Applying the model to adolescents' smoking suggests that: (a.) the response of the friendship network to changes in tobacco price amplifies the intended effect of price changes on smoking, (b.) racial desegregation of high-schools decreases the overall smoking prevalence, (c.) the peer effect complementarities are substantially stronger between smokers compared to between non-smokers, (d.) the magnitude of the spillover effects from small scale policies targeting individuals' smoking choices are roughly double compared to the scale of these policies.

Preferences over tobacco smoking and frienships


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