Best-response dynamics in directed network games

We study public goods games played on networks with possibly non-reciprocal relationships between players. These include one-sided relationships, mutual but unequal relationships, and parasitism. It is known that many learning processes converge to the game's Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. Under one-sided and parasitic relationships, best-response dynamics may cycle. The production of the locally public good of players may fail to converge to an equilibrium, making static analysis less insightful in an applied setting. In this paper we show that the strong convergence results of the undirected case are retained for two economically relevant classes of directed networks: those with transitive relative importance of players and those rescalable into networks with weak externalities