Equilibrium Existence and Uniqueness In Network Games with Additive Preferences
A directed network game of imperfect strategic substitutes with heterogeneous players is analyzed. We consider concave additive separable utility functions that encompass the quasi-linear ones. It is found that pure strategy Nash equilibria verify a non-linear complementarity problem. By requiring appropriate concavity in the utility functions, the existence of an equilibrium point is shown and equilibrium uniqueness is established with a P -matrix. Then, it appears that previous ﬁndings on network structure and sparsity hold for many more games.
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