# Nash Equilibria on (Un)Stable Networks

## TL;DR

This paper models how individuals in networks decide to change behaviors or friendships, introducing a game-theoretic framework that accounts for bounded rationality and consensus, with applications to adolescent smoking behaviors.

## Contribution

It develops a novel game-theoretic model incorporating friendship dynamics and bounded rationality, providing a probabilistic ranking of equilibria and a method for estimating such games.

## Key findings

- Friendship network responses amplify tobacco price effects on smoking.
- Racial desegregation reduces overall smoking prevalence.
- Peer effects are stronger among smokers than non-smokers.

## Abstract

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 choose their behaviors and friendships. In equilibrium, players internalize the need for consensus in forming friendships and 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.) 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.