Public goods in networks: Comparative statics results

We consider public goods games with heterogeneous players interacting on a network and investigate how shocks to players' characteristics and changes in interaction patterns influence individual and total contributions. We introduce a linear system associated to the initial game, in which heterogeneity in players' characteristics is removed and interactions between players are reversed, and show that what matters in determining the effects of a shock on contributions is the sign of the coordinates of its unconstrained solution. When players are identical, we demonstrate that positive shocks on active players increase contributions, while positive shocks on strictly inactive players decrease them, contrary to intuition. We also identify a subset of players, called neutral players, who exert no influence on total contributions. Furthermore, we provide precise formulas for the change in total contributions following various types of shocks, and provide conditions to determine whether the shock will have positive or negative consequences on contributions. We show that these conditions always rely on the sign of the associated problem's unconstrained solution coordinates of the players impacted by the shock.