Equilibrium Existence and Uniqueness In Network Games with Additive Preferences

Yann Rébillé (1) , Lionel Richefort (1)

1 LEMNA - Laboratoire d'économie et de management de Nantes Atlantique

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.

Mots clés: P -matrix; network game; additive preferences; complementarity problem

Domaines: Economies et finances; Gestion et management

Yann Rébillé, Lionel Richefort. Equilibrium Existence and Uniqueness In Network Games with Additive Preferences. 2012. ⟨hal-00732962⟩