Nash Equilibria on (Un)Stable Networks

Anton Badev

Econometrica (May, 2021)

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In response to a change, individuals may choose to follow the responses of their friends or, alternatively, choose differently and change their friends. The contrast between the choices of friends and of behaviors is not related to the presence of strategic incentives or instincts for selfish decisions. Rather, choosing a friend presumes a consent (Jackson and Wolinsky, 1996) while choosing behaviors does not (Nash, 1950).

A Nash equilibrium in a k-stable (NEkS) network emerges when players internalize the need for consent 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.

Empirical analysis of adolescents' smoking and friendships 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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