Equilibrium Uniqueness in Network Games with Strategic Substitutes

A local public goods game in weighted and directed networks is analyzed. Individual efforts are imperfect substitutes, players' preferences are heterogeneous and local externalities are non-uniform and asymmetric. Sufficient conditions under which the game admits a unique equilibrium are established in terms of the number of links between agents in the original network. It appears that these latter conditions for uniqueness are met if, and only if, the structure of relationships is \emph{productive}. That is, a parallel can be established between network games with strategic substitutes and the input-output theory pioneered by Wassily Leontief.