Cooperation and coordination in threshold public goods games with asymmetric players

In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments 𝑒𝑖, productivities 𝑝𝑖, and rewards 𝑟𝑖. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group's collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people's cooperation and coordination. We show that heterogeneity in 𝑒𝑖𝑝𝑖 can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher 𝑒𝑖𝑝𝑖 are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).