Nash Equilibria on (Un)Stable Networks
Econometrica (May 2021)
★ Smoker○ Nonsmoker— Friendship
A’s smoking choice and friendship can change together.
Abstract
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 requires 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 is roughly double the scale of these policies.
Preferences over tobacco smoking and friendships
Three players: A, B, and C.
- A wants to have friends.
- B hates smoking.
- C smokes.
Reading the diagrams: shaded stars represent smokers; circles represent nonsmokers; lines represent friendships. Each outcome is also described in text.
A’s outcomes are ranked from best to worst for each tobacco price. In the worst outcome, a slash separates A’s nonsmoking and smoking choices: either way, she is unhappy because she has no friends.
High tobacco price
- 1. Best
A does not smoke and is friends with B. C smokes and is unconnected.
- 2. Second best
A smokes and is friends with C. B is unconnected.
- 3. Worst
Whether A smokes or not, she is unhappy because she has no friends.
Low tobacco price
- 1. Best
A smokes and is friends with C. B is unconnected.
- 2. Second best
A does not smoke and is friends with B. C smokes and is unconnected.
- 3. Worst
Whether A smokes or not, she is unhappy because she has no friends.
References
Selected references and hard-to-find papers