Nash Equilibria on (Un)Stable Networks

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 nonsmokers.

Additively Separable Hedonic Games with Social Context

“…Finally, it is also worth mentioning some related literature on network formation games, in which interestingly the considered games are shown to be potential games as in our paper: in [38], Badev deals with a setting in which the utility of the players is influenced by the friendship relations and vice-versa, while Kinateder and Merlino [39] study a network creation game in which benefits are shared among neighbors. Mele [40] proposes an empirical model of social network formation, combining strategic and random connections among players.…”

The Evolution of Networks and Local Public Good Provision: A Potential Approach

“…The co-evolution of networks and behavior is a stochastic best-response dynamic similar to that of [11,12,26,27]. Time is discrete and denoted by t = 0, .…”

“…Additionally, this steady state distribution could be used to bring the model to the data, as in [11,12]. In this respect, it is important to note that we can derive this steady state distribution in the formulation of the problem, which allows for player heterogeneity.…”

“…More recently, Ref. [12] developed a similar approach for a game of strategic complements in an endogenous network, and introduced a notion of equilibrium (k-Nash) that spanned from two-sided to one-sided link formation. Additionally, Ref.…”

“…The contribution of this paper with respect to this literature is twofold. First, contrarily to [12,27], we studied a game with non-linear best-replies. As a result, we could not make use of the techniques developed by [25] to characterize the equilibrium set.…”