Nash Equilibria on k-stable Networks

Anton Badev

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"[the distinction between cooperative and non-cooperative games] depends on the possibility or impossibility of coalitions, communications, and side-payments." (Nash, 1950)

Abstract

While individuals may chose selfishly, only considering their own incentives, their optimal behaviors (Nash, 1950), they commit to relationships that result from communication, coordination, and collaboration (Jackson and Wolinsky, 1996).

In games of friendship links and behaviors, a Nash equilibrium in k-stable (NEkS) network emerges when players internalize the need for consensus in forming and sustaining human relationships. In a NEkS network, no player has profitable and permissible, by the stability constraints, deviation involving less than k links. The stability constraints guarantee that a player can form a relationship only if this relationship is beneficial for her intended friend.

A primitive of games of link and node statuses are payoff externalities and the possibility for multiple NEkS networks. NEkS networks are ranked in probabilistic sense as they arise in a k-player consensual dynamic (kCD). Properties of kCD fascilitate simulation from and estimation of these games.

Application of the proposed framework to adolescents' tobacco smoking and friendship decisions suggests that: (a.) the response of the friendship network to changes in tobacco price amplifies the intended effect on smoking, (b.) racially desegregating high-schools decreases the overall smoking prevalence, (c.) the response of the social network is quantitatively important in analyzing the aggregate spillovers, (d.) the estimation biases when the network externalities are mis-specified and when peer effects are omitted are of the same sign.

Preferences over tobacco smoking and frienships

[PHOTO]

References
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