Equilibrium Existence and Uniqueness In Network Games with Additive Preferences
AbstractA 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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Date of creation: 17 Sep 2012
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network game ; additive preferences ; complementarity problem ; P -matrix ;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-30 (All new papers)
- NEP-COM-2012-09-30 (Industrial Competition)
- NEP-GTH-2012-09-30 (Game Theory)
- NEP-HPE-2012-09-30 (History & Philosophy of Economics)
- NEP-MIC-2012-09-30 (Microeconomics)
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