Network potentials

A network payoff function assigns a utility to all participants within a social network. In this paper we investigate network payoff functions that admit an exact network potential or an ordinal network potential. We also investigate exact and ordinal potentials of Myerson’s non-cooperative network formation game based on consent in link formation. We show that the admittance of certain of these network and game-theoretic potentials implies the existence of pairwise stable networks and the convergence of network formation processes. Our main results extend and strengthen the current insights in the literature on game theoretic approaches to social network formation.

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