Evolution of cooperation in costly institutions exhibits Red Queen and Black Queen dynamics in heterogeneous public goods.

Public goods are often subject to heterogeneous costs, such as the necessary costs to maintain the public goods infrastructure. However, the extent to which heterogeneity in participation cost can affect groups' ability to provide public goods is unclear. Here, by introducing a mathematical model, I show that when individuals face a costly institution and a free institution to perform a collective action task, the existence of a participation cost promotes cooperation in the costly institution. Despite paying for a participation cost, costly cooperators, who join the costly institution and cooperate, can outperform defectors who predominantly join a free institution. This promotes cooperation in the costly institution and can facilitate the evolution of cooperation in the free institution. For small profitability of the collective action, cooperation in a costly institution but not the free institution evolves. However, individuals are doomed to a winnerless red queen dynamics in which cooperators are unable to suppress defection. For large profitabilities, cooperation in both the costly and the free institution evolves. In this regime, cooperators with different game preferences complement each other to efficiently suppress defection in a black queen dynamic.