Title: Spatial interactions and oscillatory tragedies of the commons,
Abstract: A tragedy of the commons (TOC) occurs when individuals acting in their own
self-interest deplete commonly-held resources, leading to a worse outcome than
had they cooperated. Over time, the depletion of resources can change
incentives for subsequent actions. Here, we investigate long-term feedback
between game and environment across a continuum of incentives in an
individual-based framework. We identify payoff-dependent transition rules that
lead to oscillatory TOC-s in stochastic simulations and the mean field limit.
Further extending the stochastic model, we find that spatially explicit
interactions can lead to emergent, localized dynamics, including the
propagation of cooperative wave fronts and cluster formation of both social
context and resources. These dynamics suggest new mechanisms underlying how
TOCs arise and how they might be averted.