Grazing Games: Sharing Common Property Resources with Complex Dynamics

Grasslands used for domestic livestock are often the common property of several owners and are typically characterized by complex ecosystem dynamics. We account for both these aspects by modeling the problem as a differential game where each farmer maximizes profits, given the dynamics of livestock and grass interaction. We compare the first best outcome obtained when farmers cooperate with that for non-cooperative farmers. By accounting for grassland dynamics, we challenge conventional results from the common pool literature. Although we do identify situations where the standard result holds—a tragedy of the commons unless farmers cooperate—we also find examples where a tragedy is exacerbated due to ecosystem dynamics as well as cases where a non-cooperative regime under-exploits the grassland compared to the first best outcome.